school of engineering and sciences an integral approach
TRANSCRIPT
Instituto Tecnológico y de Estudios Superiores de Monterrey
Campus Ciudad de México
School of Engineering and Sciences
An integral approach for the synthesis of optimum operating procedures of thermal power plants towards better operational flexibility.
A dissertation presented by
Erik Rosado Tamariz
Submitted to the
School of Engineering and Sciences in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
In
Engineering Science
Principal Advisor: Rafael Batres Prieto Co-advisors: Alfonso Campos Amezcua and Diego Ernesto Cárdenas Fuentes
Mexico City, June 11th, 2020
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Dedication
To my parents Carmelo Rosado Mojica and Teodora Tamariz González, for being the
best example in life, and for all their love, trust, support, and effort. Thank you for teaching
me the value of love, honesty, humility, gratitude, discipline, and hard work in life.
To my son José Alain and my daughter Christian America for being the engine that drives
me, my motivation, the source of my inspiration, and my balance. For all the teachings
and life experiences. For being unconditional with me, for all your support, love, and for
trusting me.
To my wife Christian, my life partner, my best friend, and my accomplice. Thank you for
always giving me your support, trust, and words of encouragement. Thank you for being
with me and supporting me in all those moments of success, but especially in those
difficult ones. Simply because without you, I don't know if I would have made it.
Live as if you were to die tomorrow. Learn as if you were to live forever.
Mahatma Gandhi
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Acknowledgements
This thesis for the Doctor of Philosophy in engineering science degree was completed
thanks to the support in the tuition granted by the Tecnologico de Monterrey and thanks
to the support for living granted by the Consejo Nacional de Ciencia y Tecnologia
(CONACYT).
To the Tecnológico de Monterrey for allowing me to live this experience, and work
with great people including colleagues, professors, teachers, and students. For allowing
me to develop my research in the Project 266632 “Bi-National Laboratory on Smart
Sustainable Energy Management and Technology Training”, funded by the CONACYT
SENER Fund for Energy Sustainability (Agreement: S0019201401).
I would like to express a special thanks to the National Institute of Electricity and Clean
Energies (INEEL) for their financial support. To the mechanical systems division and its
directors Dr. José Miguel González Santaló (†) and Dr. Eduardo Preciado Delgado for
trusting me and allowing me to continue growing professionally with this doctorate. To the
Managers Dr. Ulises Mena Hernandez and MSc. Alonso Alvarado Gonzaléz for giving me
this opportunity.
I would like to express my gratitude to my main advisor, Dr. Rafael Batres who helped
me lay the basis for this research, guided me and provided me with the necessary tools
to develop this research. For all your advice and your perseverance. Thanks for allowing
me to work in his research group.
To my advisors at the INEEL Dr. Zdzislaw Mazur and Dr. Alfonso Campos for all their
support, advice, and suggestions. For contributing all their experience of the energy
sector to development and improvement of this research. To my co-advisor Dr. Diego
Cardenas for promoting hard and structured work in me, for their constructive criticism
and patience. To my committee member, Dr. Ricardo Ganem, for his comments and
guidance on this work.
To Professor Dr. Filippo Genco for allowing me to participate in his research group
during my research stay at the Universidad Adolfo Ibáñez, as well as his support and
suggestions to complete and extend the scope of this research. I also appreciate the help
and technical support received by the researchers of Adolfo Ibanez University and in
particular of engineers Macarena Montane’ and Luis Campos.
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I would like to express special gratitude to my colleagues in the research group Miguel
Ángel, Luis Enrique, Sara, Emilio y Rodrigo who support me in those difficult moments
and enjoying the achievements with me. Particularly to Miguel Ángel who support me in
the development of the research and contributed valuable ideas to improve my research,
and to Emilio for your contribution to the implementation of the optimization algorithm.
To the Agencia Chilena de Cooperacion Internacional para el Desarrollo who, through
the Plataforma de Movilidad Estudiantil y Académica de la Alianza del Pacífico
scholarship, provided the necessary support for conducting a doctoral research internship
at the Universidad Adolfo Ibáñez, thus allow performing and successfully completing this
research project.
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An integral approach for the synthesis of optimum operating procedures of thermal power plants towards a better operational
flexibility by
Erik Rosado Tamariz Abstract
To deal with the challenge of a balance between the large-scale introduction of variable renewable energies and intermittent energy demand scenarios in the current electrical systems, operational flexibility plays a key role. The electrical system operational flexibility can be addressed from different areas such as power generation, transmission and distribution systems, energy storage (both electrical and thermal), demand management, and coupling sectors. Regarding power generation, specifically at the power plant level, operational flexibility can be managed through the cyclic operation of conventional power plants which involve load fluctuations, modifications in ramp rates, and frequents startup and shutdowns. Since conventional power plants were not designed to operate under cyclic operating schemes with involve fast response times, must develop these capabilities through the design of operating procedures that minimize the time needed to take the power plant from an initial state to the goal state without compromising the structural integrity of critical plant components. This thesis proposes a dynamic optimization methodology to the synthesis of optimum operating procedures of thermal power plants which determine the optimal control valves sequences that minimize its operating times based on techniques of dynamic simulation, metaheuristic optimization, and surrogate modeling. Based on such an approach, the power plants must be increasing its operational flexibility to address a large-scale introduction of variable renewable energies and intermittent energy demand scenarios. This thesis proposes a dynamic optimization framework based on the implementation of a metaheuristic optimization algorithm coupled with a dynamic simulation model, using the modeling and simulation environment OpenModelica and a surrogate model to estimate in a computationally efficient way the structural integrity constraint of the dynamic optimization problem. Two case studies are used to evaluate the proposed framework by comparing their results against information published in the literature. The first case study focuses on managing the thermal power plant's flexible operation based on the synthesis of the startup operating procedure of a drum boiler. The second case study addresses the synthesis of an optimum operating strategy of a combined heat and power system to improve the electric power system’s operational flexibility.
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List of Figures Figure 1.1. Demand profiles of the Mexican National Electric Power System 2018-2019 based on [3]. ................................................................................................................. 17
Figure 1.2. Comparison of baseline demand profile with respect to scenarios of shifting and shedding demand due to controllable and unexpected factors, based on [6]. ........ 18
Figure 1.3. Comparison of solar photovoltaic power plant daily generation profiles for sunny and cloudy days, based on [12]. ......................................................................... 19
Figure 1.4. Comparison of solar photovoltaic power plant daily generation profiles for sunny and cloudy days, based on [12]. ......................................................................... 20
Figure 1.5. Demand profile for an electric power system with high variable renewable generation penetration, based on [12]. .......................................................................... 21
Figure 1.6. Mexican electric power system total installed capacity distribution by technology, based on [14]. ............................................................................................ 22
Figure 1.7. Power plant ramp rate definition. Based on data from [24].......................... 25
Figure 1.8. Power plant ramp rate definition based on [24]. .......................................... 26
Figure 1.9. Spiral model adaptation proposed, based on [29]. ...................................... 32
Figure 2.1. World gross electricity production, by source, 2017, based on [32]. ........... 36
Figure 3.1. Implementation of the framework. ............................................................... 55
Figure 3.2. Operation diagram of the mGA. .................................................................. 57
Figure 3.3. Example of a random population of four individuals. ................................... 58
Figure 3.4. Graphical representation of the crossover genetic operator in the mGA. .... 59
Figure 3.5. Graphical representation of the crossover genetic operator in the mGA. .... 59
Figure 3.6. The new population after the crossover and mutation operators. ................ 60
Figure 3.7. An example of the fitness associated with each member of the population. 60
Figure 3.8. An example of the selection of the best individual of the population. .......... 61
Figure 3.9. An example of the selection of the best individual of the population. .......... 61
Figure 3.10. An example of the selection of the best individual of the population. ........ 62
Figure 3.11. Operating scheme of the SATAS hybrid optimization. .............................. 62
Figure 3.12. Operation diagram of the seed generation algorithm. ............................... 63
Figure 3.13. Randomly generated procedures. ............................................................. 63
Figure 3.14. Mutation process from one to four mutations. ........................................... 65
Figure 3.15. Optimization process operation. ................................................................ 66
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Figure 3.16. Operation diagram of the SATAS hybrid optimization algorithm. .............. 67
Figure 3.17. Example of five neighbors (one mutation) from an actual solution. ........... 67
Figure 3.18. Probability of neighbor solution (better and worse) of becoming the new actual solution. .............................................................................................................. 68
Figure 4.1. A drum boiler basic configuration. ............................................................... 71
Figure 4.2. A drum boiler’s basic configuration. ............................................................ 72
Figure 4.3. Drum boiler simulator in OpenModelica. ..................................................... 77
Figure 4.4. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of heat supplied. ........................................... 78
Figure 4.5. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of the steam regulator valve position. ........... 78
Figure 4.6. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of the output steam from the drum boiler. .... 79
Figure 4.7. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of the pressure in the drum boiler. ................ 79
Figure 4.8. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of the steam temperature in the drum boiler. 80
Figure 4.9. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of the thick-walled von Mises stresses. ........ 80
Figure 4.10.A combined cycle power plant basic configuration. .................................... 84
Figure 4.11. Gas turbine structure. ................................................................................ 85
Figure 4.12. The basic configuration of a HRSG with one pressure level. .................... 86
Figure 4.13. Steam line schematic representation. ....................................................... 87
Figure 4.14. Schematic diagram of a steam turbine. ..................................................... 88
Figure 4.15. Schematic diagram of a power plant condenser. ...................................... 89
Figure 4.16. CHP system based on hot exhaust gases, based on [127]. ...................... 91
Figure 4.17. CHP system based on low-pressure steam, based on [127]. .................... 91
Figure 4.18. Operating scheme of a CHP system based on energy recovery from the hot exhaust gas. .................................................................................................................. 92
Figure 4.19. The basic configuration of combined heat and power systems based on high-temperature exhaust gases. .......................................................................................... 94
Figure 4.20. Combined cycle power plant simulator in OpenModelica graphical environment. ............................................................................................................... 105
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Figure 4.21. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of gas turbine mechanical power. ......................................................................................................................... 106
Figure 4.22. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of low-pressure steam turbine mechanical power. ...................................................................................................... 106
Figure 4.23. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of intermediate pressure steam turbine mechanical power. ................................................................................ 107
Figure 4.24. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of high-pressure steam turbine mechanical power. .......................................................................................... 107
Figure 4.25. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of gas turbine exhaust gas temperature. ................................................................................................................ 108
Figure 4.26. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of high-pressure drum boiler level. ............................................................................................................................ 108
Figure 4.27. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of intermediate pressure drum boiler level. .................................................................................................................. 109
Figure 4.28. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of low-pressure drum boiler level. ............................................................................................................................ 109
Figure 4.29. Exhaust Gas Splitter System (EGBS) proposed for the CHP system in the OpenModelica graphical environment. ........................................................................ 111
Figure 4.30. Heating circuit features of the electrowinning plant based on [149]. ....... 113
Figure 4.31. Combined heat and power simulation model – OpenModelica. .............. 114
Figure 4.32. Splitter location feasibility in terms of energy consumption. .................... 116
Figure 4.33. Splitter location feasibility in terms of flue gas temperatures. .................. 116
Figure 4.34. Exhaust gases flow profiles for CCPP and CHP System. ....................... 119
Figure 4.35. Mechanical power profiles for CCPP and CHP System. ......................... 119
Figure 5.1. A superheater basic configuration [153]. ................................................... 123
Figure 5.2. The superheater header surrogate model implementation flowchart. ....... 125
Figure 5.3. Finite element model of the superheater header with mesh refinement in the vicinity of nozzles holes. .............................................................................................. 128
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Figure 5.4. Heat transfer boundary conditions in the superheater header nozzle’s holes and inner surfaces. ...................................................................................................... 130
Figure 5.5. Heat transfer boundary conditions in the external surfaces....................... 130
Figure 5.6. Header temperature distribution for the FEM heat transfer analysis. ........ 131
Figure 5.7. Mechanical load in terms of pressure on the inner cylinder and on the surfaces of the nozzle holes of the header. ............................................................................... 131
Figure 5.8. Normal von Mises stress distribution in the header under unit thermal load. .................................................................................................................................... 132
Figure 5.9. Normal von Mises stress distribution in the header under unit mechanical load. .................................................................................................................................... 133
Figure 5.10. Thermal and mechanical load curve in terms of the steam pressures and temperatures for the transient analysis. ...................................................................... 135
Figure 5.11. Temperature evolution in the inner and outer surfaces of the header during heat transfer transient analysis. .................................................................................. 136
Figure 5.12. Thermal and mechanical stresses evolution in the header for structural transient analysis......................................................................................................... 137
Figure 5.13. Comparison of thermal stresses distributions between the unit static analysis and some simulation times at the beginning of the transient analysis. ........................ 138
Figure 5.14. Comparison of thermal stresses distributions between the unit static analysis and some simulation times at the end of the transient analysis. ................................. 139
Figure 5.15. Comparison of mechanical stresses distributions between the unit static analysis and some simulation times at the beginning of the transient analysis. .......... 140
Figure 5.16. Comparison of mechanical stresses distributions between the unit static analysis and some simulation times at the end of the transient analysis..................... 141
Figure 5.17. Thermal stresses evolution in the header. A comparison is made between structural transient analysis and their corresponding stresses escalation based on the unit static analysis. ............................................................................................................. 142
Figure 5.18. Mechanical stresses evolution in the header. A comparison is made between structural transient analysis and their corresponding stresses escalation based on the unit static analysis. ............................................................................................................. 142
Figure 5.19. Failure-prone critical zone in the header. ................................................ 144
Figure 5.20. Header stress response surface under unit thermal load. ....................... 145
Figure 5.21. Header stress response surface under unit mechanical load. ................. 145
Figure 5.22. Response surface scaled according to the pressure differential in the header. .................................................................................................................................... 147
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Figure 5.23. Response surface scaled according to the header differential temperature. .................................................................................................................................... 148
Figure 5.24. Graphical representation of the configuration of the neural net model. ... 150
Figure 5.25. Graphical representation of the neural network model of the thermal response surface. ........................................................................................................ 153
Figure 5.26. Graphical representation of the neural network model of the mechanical response surface. ........................................................................................................ 153
Figure 5.277. Comparison of times in minutes to assess the structural integrity constraint in the dynamic optimization problem using different models. ...................................... 155
Figure 6.1. Comparison of the distance from the current state to the goal state overtime for the drum boiler startup optimization obtained with mGA (dotted lines) and SATAS (solid lines). ................................................................................................................. 160
Figure 6.2. Results comparison between the curves of the operating benchmark profile developed by Åström & Bell, the optimized profiles reported by Franke et al. and Belkhir et al., and the proposed approach mGa and SATAS for the power generated. .......... 161
Figure 6.3. Results comparison between the curves of the operating benchmark profile developed by Åström & Bell, the optimized profiles reported by Franke et al. and Belkhir et al., and the proposed approach mGa and SATAS for the steam that exits of the system. .................................................................................................................................... 161
Figure 6.4. Results comparison between the curves of the operating benchmark profile developed by Åström & Bell, the optimized profiles reported by Franke et al. and Belkhir et al., and the proposed approach mGa and SATAS for the pressure in the drum boiler. .................................................................................................................................... 162
Figure 6.5. Results comparison of the operating profile of the steam regulating valve between the models Åström & Bell, Franke et al. and Belkhir et al. ............................ 163
Figure 6.6. Results comparison of the optimized operating profile of the steam regulating valve based on the proposed approach using mGa and SATAS algorithms. .............. 163
Figure 6.7. Results comparison of the operating profile of the heat flow supplied to the system between the models Åström & Bell, Franke et al., and Belkhir et al. ............... 164
Figure 6.8. Results comparison of the optimized operating profile of the heat flow supplied to the system based on the proposed approach using mGa and SATAS algorithms. . 164
Figure 6.9. Results comparison between the curves of the operating benchmark profile developed by Åström & Bell, the optimized profiles reported by Franke et al. and Belkhir et al., and the proposed approach mGa and SATAS for the thick-walled von Mises stress. .................................................................................................................................... 165
Figure 6.10. Steam turbines operational data of the San Isidro II combined cycle power plant for the 2018 year. ............................................................................................... 169
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Figure 6.11. Normalized operating scheme of the CHP system during the cyclic operation case study. .................................................................................................................. 171
Figure 6.12. Gas turbine exhaust gases flow regulation system in the CHP system. .. 173
Figure 6.13. Gas turbine exhaust gases flow required by the cogeneration system (blue) and flow available for the operation of steam turbines (red) in the case of a cyclic operation study. ........................................................................................................................... 176
Figure 6.14. Profiles of temperature and enthalpy of the electrolytic solution during the cyclic operation case study of the San Isidro II combined cycle power plant coupled to a cogeneration plant. ...................................................................................................... 177
Figure 6.15. Control profiles of the regulating valve for the gas turbine exhaust gases in the electrowinning process inlet during the cyclic operation case study of the San Isidro II combined cycle power plant coupled to a cogeneration plant. ................................. 177
Figure 6.16. Comparison of the distance from the current state to the goal state overtime for the baseline case study (blue) and optimized profile using the SATAS optimization algorithm for the cyclic operation case study. .............................................................. 178
Figure 6.17. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the power generated in the steam turbines. ........................................................... 179
Figure 6.18. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the steam pressure at the high-pressure evaporator outlet. ................................... 179
Figure 6.19. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the steam temperature at the high-pressure evaporator outlet. ............................. 180
Figure 6.20. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the throttle valve that regulates the steam flow that enters the HP superheaters... 181
Figure 6.21. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the ramping rate of flow flue gases in the Heat Recovery Steam Generator (HRSG). .................................................................................................................................... 181
Figure 6.22. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the thermomechanical stresses in critical zone 1 that are prone to failure. ............ 182
Figure 6.23. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the thermomechanical stresses in critical zone 2 that are prone to failure. ............ 183
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Figure 6.24. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the power generated in the gas and steam turbines. ............................................. 184
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List of Tables Table 1.1. Operational flexibility features of thermal power plants [28]. ........................ 27
Table 3.1. Relation between feasibility scale and number of mutations in the operating procedure for an example of 9 genes. ........................................................................... 64
Table 4.1. Electrowinning process characterization [149]. .......................................... 113
Table 4.2. Exhaust gases operating parameters for a load change simulation. .......... 115
Table 4.3. Cogeneration system operating parameters for full load gas turbine. ........ 118
Table 5.1. Superheater header features. ..................................................................... 127
Table 5.2. Header convection heat transfer coefficients. ............................................. 129
Table 5.3. Structure of the inputs and outputs for ANN model. ................................... 151
Table 5.4. Accuracy of the ANN model for the evaluation of the structural integrity constraint in the superheater header. .......................................................................... 151
Table 5.5. Comparison of times to assess the structural integrity constraint in the dynamic optimization problem using different models. .............................................................. 155
Table 6.1. Combinations of the heat flow rate and steam flow rate for each action. ... 158
Table 6.2. Comparison of the useful life consumption and fatigue damage in the drum boiler for all startup profiles evaluated in the case study 1. ......................................... 166
Table 6.3. Combinations of the heat flow rate in the HSRG inlet and steam flow rate in the superheater for each action. .................................................................................. 175
Table 6.4. Comparison of the useful life consumption and fatigue damage in the superheater header for the cyclic operation case study of the combined cycle power plant coupled to a cogeneration plant. ................................................................................. 184
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Contents Declaration of Authorship ............................................................................................. 1
Dedication .................................................................................................................... 2
Acknowledgements ...................................................................................................... 3
Abstract ........................................................................................................................ 5
List of Figures .............................................................................................................. 6
List of Tables .............................................................................................................. 13
1. Chapter one ........................................................................................................... 16
Introduction ................................................................................................................ 16
1.1 Background ................................................................................................... 16
1.2 Problem statement ........................................................................................ 28
1.3 Research questions ...................................................................................... 29
1.4 Hypothesis .................................................................................................... 30
1.5 Objectives ..................................................................................................... 31
1.6 Research methodology ................................................................................. 32
1.7 Thesis outline ................................................................................................ 34
2. Chapter two ........................................................................................................... 36
Literature review ........................................................................................................ 36
2.1 Thermal power plants ................................................................................... 36
2.2 Approaches to improve operational flexibility ................................................ 38
3. Chapter three ........................................................................................................ 53
Dynamic optimization framework ............................................................................... 53
3.1 Introduction ................................................................................................... 53
3.2 Proposed approach ....................................................................................... 54
4. Chapter Four ......................................................................................................... 69
Simulation models ...................................................................................................... 69
4.1 Introduction ................................................................................................... 69
4.2 Drum boiler modeling .................................................................................... 70
4.3 Modeling of Combined Cycle Power Plants (CCPP) and Combined Heat and Power Systems (CHP) ............................................................................................ 81
5. Chapter Five ........................................................................................................ 121
Surrogate modeling .................................................................................................. 121
5.1 Introduction ................................................................................................. 121
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5.2 The superheater.......................................................................................... 123
5.3 Surrogate modeling ..................................................................................... 124
6. Chapter Six .......................................................................................................... 156
6.1 Case study 1: Synthesis of the startup operating procedure of a drum boiler 156
6.2 Case study 2: Synthesis of an optimum operating strategy of a CHP system 168
7. Chapter Seven..................................................................................................... 186
Conclusions and Future Work .................................................................................. 186
References............................................................................................................... 190
8. Appendix A .......................................................................................................... 202
Published papers ..................................................................................................... 202
Curriculum Vitae ...................................................................................................... 207
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1. Chapter one Introduction 1.1 Background Worldwide, electric power systems are undergoing large structural changes. Commonly,
these systems are based on centralized models in which fossil-fuel-based electric power
generation prevailed. Nowadays, electric power systems are evolving towards liberalized
energy markets in which part of the electricity demand tends to be met by variable
renewable energy sources [1]. International commitments on climate change,
development of public policies, and the increasing competitiveness of energy generation
based on variable renewable energy sources have been the main drivers of the electric
power systems transition [2]. In this context, it is essential to consider the whole electric
power system's operational capabilities to integrate, in an efficient way the generation
based on variable renewable technologies. Also, factors related to the operation of the
electric power system must be taken into account, such as the variability in the electrical
power demand, which can cause instabilities in the power network. Such variability in
electrical power demand may be due to consumption factors since the users consume
electrical power according to their needs and have no evident consumption patterns;
consumers can change their load throughout the day, week, and months of the year. An
electric power system intermittence induced by the variable consumption of electricity can
be exemplified by electrical power demand profiles. Figure 1.1 shows the demand profiles
of the Mexican National Electric Power System (SEN) on different days for twelve months
2018-2019 [3].
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Figure 1.1. Demand profiles of the Mexican National Electric Power System 2018-2019 based on [3].
Due to current technological impediments for the storing of energy in massive
quantities and the need for the electric power system to operate synchronically, the
electrical power generation, and the system energy demand must be balanced in real-
time (illustrated in Figure 1.1). Thus, the electric power system operator (PSO)1 is always
responsible to coordinate power generation of all power units available to match energy
supply with demand, guaranteeing safe, stable, and economic operation of the electric
power system. In Mexico, the system operator is the Centro Nacional de Control de
Energía (CENACE) [4]. Operational management of electrical power units is carried out
in a planned way, following well-studied and predicted demand patterns albeit the
presence of exceptional events that can induce operational variations to the system.
These events can be predictable or spontaneous. As a result, the electric power system
must be able to respond to these needs efficiently without compromising the quality and
continuity of electric power supply.
1 The PSO is responsible for managing and monitoring the power grid in order to anticipate and mitigate potentially dangerous and costly system problems, and when a power grid disturbance occur, its function is to restore it to safe operating conditions efficiently [5].
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Other causes of variability include unforeseen failures in power units, transmission
or distribution lines, substations or transformers, as well as disconnection of many
electricity consumers of the power grid at the same time. Likewise, events such as a
holiday, musical concerts, or high-attendance sports events can also generate significant
levels of variability. Based on [6], a comparison for an electric power system baseline
demand profile with respect to shifting and shedding demand scenarios due to
controllable and unexpected factors is shown in Figure 1.2.
Figure 1.2. Comparison of baseline demand profile with respect to scenarios of shifting and shedding demand due to controllable and unexpected factors, based on [6].
In this way, electric power systems are provided with an inherent capability of
operational flexibility, which allows them to deal successfully with the variability and
uncertainty challenges in order to balance the electrical power supply and energy demand
efficiently.
Another source of variability is the result of the introduction of large-scale variable
renewable energy, which has its own variability in power generation. According to [7],
deployment of power plants based on variable renewable sources such as wind, and solar
energy are achieving a key role in new electric power systems. This because of the
development of variable renewable energy technologies have reached a good
19
technological level promising a bright future for electric power systems and with highly
competitive generation costs [8]. Likewise, the combined effect of the energy variable
demand coupled with the increasing adoption of variable renewable power plants makes
it difficult to reach a supply-demand balance.
As reported by [9-11], non-conventional renewable generation or variable
generation are those power generation technologies from renewable primary resources
whose availability and intensity varies significantly with weather conditions and time
scales. Examples are wind and solar energy, which are the most mature and widely
employed technologies. Therefore, these technologies cannot operate at this time as a
traditional dispatchable generator due to variable generation nature and its dependence
on weather conditions. The variable and intermittent behavior of these power plants can
be illustrated through their daily generation profiles for typical periods of generation.
Figure 1.3 shows the generation profiles of a solar photovoltaic power plant, produced
during sunny and cloudy days (based on data available in [12]). Figure 1.4 illustrates a
month of electrical power generation for a couple of onshore wind power plants currently
in operation [12].
Figure 1.3. Comparison of solar photovoltaic power plant daily generation profiles for sunny and cloudy days, based on [12].
20
Electrical power generation in solar photovoltaic power plants is restricted by the
time of day, being unable to generate energy during the night hours. Also, solar power
generation is constrained by weather conditions such as cloudy days, resulting in
generation profiles with repetitive patterns and frequent ramps up and down during the
operation period. It should be noticed that the individual impact of these power plants is
minimal for the electric power system in terms of possible imbalances between supply
and demand, but their large-scale introduction could induce significant instabilities and
operational risks to the system.
Figure 1.4. Comparison of solar photovoltaic power plant daily generation profiles for sunny and cloudy days, based on [12].
While daily solar photovoltaic generation profiles have slight differences in terms
of shape and pattern, wind power generation has greater variability regarding its primary
source intensity and availability. As shown in Figure 1.4, wind energy must deal with the
challenge of intraday2 variability, as well as the contrast of maximum generation levels for
each day.
2 In the intraday market, buyers and sellers can trade power close to real time to balance the supply and demand of power [13].
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Since the generation based on variable renewable technologies cannot be
controlled, they must be dispatched whenever their primary energy source is available:
this drives the electrical system operator to manage conventional generation in such a
way that wind and solar energy are supplied first. This requires a higher level of electrical
power system operational flexibility to guarantee a safe, stable, and economic operation
of the electrical grid. In other words, conventional power-generation plants should
efficiently dispatch generation to variable and uncertain demand profiles. In the operation
of electric power systems involving variable renewable technologies, demand curves are
usually studied as net demand profiles or residual loads, where net demand corresponds
to the instantaneous difference between demand and variable renewable generation.
Thus, a net demand profile helps to visualize the combined variability due to both the
demand and the variable renewable generation.
Figure 1.5 shows a net demand curve based on data from [12], which highlights
some challenges that arise when the demand variability coexists in an electrical system
with a high contribution of variable renewable generation (wind and solar energy).
Figure 1.5. Demand profile for an electric power system with high variable renewable generation penetration, based on [12].
22
As shown in Figure 1.5, different levels of adjustment between the electric power
system demand (in red) and variable renewable generation (in green) can lead to more
abrupt variations in the electric power system's net demand (in blue). Therefore, achieving
a net demand profile balance safely and at a minimum cost is the main challenge for
integrating systems based on variable renewable generation. In accordance with the
increasing incorporation of variable renewable generation technologies in the electric
power systems, variations in net demand are growing, giving rise to unprecedented ramp
requirements and even risks variable renewable overgeneration.
The National Electric System in Mexico for 2018 had 6,585 MW installed of variable
renewable energy generation, of which 4,485 MW correspond to wind power plants and
1,820 MW to solar photovoltaic generation. The variable renewable technologies
represent 9.4% of the total installed capacity of the electric power system of 70,053 MW
total [14]. The distribution of the total installed capacity of the Mexican electric power
system by technology is shown in Figure 1.6.
Figure 1.6. Mexican electric power system total installed capacity distribution by technology, based on [14].
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1.1.1 Operational flexibility The inherent intermittency of power generation based on variable renewable energy
sources coupled with the electric power demand variability leads to improved response
and adjustment capabilities of the electric power systems. According to [15–17], these
capabilities are known as “power system operational flexibility”, which describe the ability
of the power system to achieve a balance between generation and demand at all times.
In other words, the electric power system should have the ability to respond properly
under short-term operational uncertainties and variabilities to avoid substantial
instabilities and economic losses.
As reported by the International Renewable Energy Agency (IRENA) [18], to
effectively manage large-scale variable renewable energy, flexibility sources must be
analyzed and planned in all-electric power system components. In this way, all potential
sources of flexibility should be investigated, and all energy systems must be considered.
In this sense, power generation, transmission and distribution systems, thermal and
electrical storage, demand management, and coupling systems are considered.
In the context of power generation, operational flexibility can be achieved through
unit commitment and plant-level operations. Unit Commitment [19] consists of finding the
optimal operational schedule of each generating unit under different constraints and
environmental conditions. Electric power is managed by solving an optimization problem
that answers the fundamental questions of when, how, and how much energy must be
generated in each power unit according to the electrical grid needs and interactions with
the power plants set managed at the time. Also, power system operational flexibility can
be managed using a power plant level approach [20]. In this approach, the problem is
addressed as an operational design strategy using advanced optimization and control
techniques that focus to minimize the operating times and maximizing the system’s
capabilities to work under cyclic operating conditions3 and peak loads. Plant-level
operations aim at deciding in real-time how much, when and under what operating
conditions it is suitable to generate electricity to increase its competitiveness and
3 Cyclic operation or cycling refers to the operation of electric generating units at varying load levels (power demand), including on/off and low load variations, in response to changes in system load (demand) requirements. Every time a power plant is turned off and on, the boiler, steam lines, turbine, and auxiliary components go through unavoidably large thermal and pressure stresses, which cause damage [21].
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profitability, according to energy market conditions and electrical grid requirements. Cyclic
operation is the most common way to achieve operational flexibility [21].
Power plants suitable for more flexible operation generally correspond to
hydropower plants, gas turbines, internal combustion, and combined cycle power plants.
Hydropower plants have one of the greatest capacities for cyclic operation and have been
a leading actor providing operational flexibility in worldwide electric power systems.
However, they are limited to favorable hydrology scenarios and water resource
availability, which are closely related to climate change. Regarding the most efficient
conventional thermal power plants, these were generally designed to operate at
baseload. Nevertheless, the growing development of variable renewable generation in
the last decades has promoted radical modifications to their operating regime to provide
operational flexibility to electrical systems with encouraging results [22].
Thermal power plants can provide flexibility as a function of its installed capacity
and according to the next constraints:
– Which are the loads in which it can operate the plant in a stable and
efficient way?
– How fast can the plant modify its load or generate power at partial load?
– How fast can the plant startup or shutdown? There are two main operation regimes that determine the capacity of thermal
power plants to operate under a cyclic operation regime to provide operational flexibility
to the electric power system turndown and ramping: turndown and plant ramping.
The turndown is an operation regime in which the plant is at a low load condition.
The turndown ratio determines the operational range of the plant and it is defined as the
ratio of the maximum capacity Pmax to minimum capacity Pmin [23]. Thus, a power plant
with a higher operating range can be operated in a greater range of feasible dispatches,
providing greater flexibility to the electric power system [24]. These limits are important
because any load change should occur without compromising the integrity of any of the
components of the plant and within the established flexibility limits.
Power plant ramping instead is an operation regime in which the plant generation
changes from an initial load to a final load. The rate of change of plant load is determined
by its ramp rate [24]. This parameter is expressed in terms of power per time (MW/min).
25
In other words, the ramp rate describes the maximum speed with which the power plant
can change the power load at a new level (higher or lower). Thus, a power plant offers
greater flexibility to the system when having a greater ramp capacity as it can respond
more quickly to surges in the system: the higher the power plant’s ramp rate, the higher
its potential to meet fluctuating demand [25]. Therefore, the ramp rates determine the
power plant startup and shutdown times. The power plant ramp rate capacity is illustrated
graphically in Figure 1.7.
Figure 1.7. Power plant ramp rate definition. Based on data from [24].
The startup time is defined as the transition period when the plant is taken from a
non-operating state to an operating state. Conversely, shutdown refers to the process in
which the plant is taken from operational to non-operational state [26]. Thermal power
plants startup and shutdown are limited mainly by the minimum times that a power plant
must keep operating after startup or remain out of operation after a shutdown, in order
not to compromise the integrity of its components. These periods are known as the
minimum uptime and minimum downtime, respectively [24]. Startup and shutdown are
dynamic processes that are strongly related to state variables of the working fluid.
According to [27], thermal power plants startup procedures can be mainly defined as a
26
function of three downtime states preceding the re-start of the unit, which are listed as
follow:
Hot startup: less than 8 hours after shutdown.
Warm startup: between 8 and 60 hours after shutdown.
Cold startup: more than 60 hours after shutdown.
Thereby, by decreasing the power plant startup times, greater flexibility of the
electric power system can be achieved. A characteristic thermal power plant startup and
shutdown profiles are illustrated in Figure 1.8.
Figure 1.8. Power plant ramp rate definition based on [24].
A comparison of the thermal power plant's operational flexibility capabilities based
on the evaluation of the three main technological parameters of cyclic operation
(turndown, ramp rate, and operating times) is presented in Table 1 [28].
27
Table 1.1. Operational flexibility features of thermal power plants [28].
Technology Minimum power output (% Pmax)
Ramp rate (% Pmax/min)
Hot startup time (min)
RE Geothermal 15 5 90
Bioenergy 50 8 180 Concentrating Solar Power 25 6 150
Dispatchable Non-RE
Coal fired 30 6 180 Lignite 50 4 360
Steam plants (fuel oil, gas) 30 7 180 Simple cycle gas turbine 15 20 10
Gas turbine combined cycle 20 8 120
From these results, it can be noticed that gas turbines and combined cycle power
plants are better suited to operate in a cyclic operation regime since they operate with
higher ramping rates and lower minimum loads that are the main features of cyclic
operation schemes in conventional thermal power plants.
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1.2 Problem statement
This thesis focuses on how the plant’s generation changes from an initial load to a final
load in a minimum time possible to meet a fluctuating demand worsen by the accelerated
growing penetration of variable renewable energies and intermittent energy demand
conditions into the market.
Methodologies that involve both the development of advanced control strategies,
as well as coupled simulation and optimization systems are proposed to guide and
facilitate the design of thermal power plants operating profiles. Some representative
studies are described in Chapter 2. Such research is based on thermodynamic modeling
to determine the startup profiles that maximize plant efficiency. However, these
optimization problems do not deal with how power plant control valves must be operated
to take the power plant to the desired goal state in minimum time. Likewise, these works
do not address load changes in operating conditions or sudden energy supply scenarios
due to electrical grid requirements.
The main limitation to design faster thermal power plants operating profiles is
related to the structural integrity of power plant critical components due to sudden
changes in the state variables. To avoid hazardous scenarios in which the proposed
profiles could result in a decrease in material useful life, the steam temperature, and
steam pressure must be monitored. It is important to note that temperature and pressure
variations must be held within the given limits to avoid high thermomechanical stresses
on the thick-walled devices which in turn cause an increment of alternating tension-
compression stresses leading to fatigue or even material failures. The different methods
and techniques focused on quantifying the thermomechanical stress and estimate the
useful life consumption of these components are described in Chapter 2. These research
studies are mainly based on well-known methods that usually not consider complex
geometrical effects nor advanced numerical computational techniques, as they can be
computationally expensive in dynamic optimization problems. Therefore, an accurate and
computationally efficient evaluation method plays an important role in the optimal design
of a thermal power plant´s operating procedures.
29
1.3 Research questions How to carry out the synthesis of optimum operating procedures of thermal power plants
taking into account the process control valve's actions and in a computationally efficient
way to improve the electric power system flexibility to deal with the challenge of large-
scale introduction of variable renewable energies and intermittent energy demand
scenarios?
To answer this research question in a comprehensive manner, some specific
issues must be addressed:
– How to synthesize operating procedures of thermal power plants that
minimize startup times without compromising the structural integrity of
critical components?
– How to synthesize operating procedures of thermal power plants that
minimize load change times without compromising the structural integrity of
critical components?
The last research question triggers the following related question:
– Assuming a dynamic optimization approach, what is the best way to
evaluate the structural integrity of critical components in a computationally
efficient way?
To efficiently address these research questions, the operational parameters of the
thermal power plant that realizes the electric power system's operational flexibility must
be identified first.
30
1.4 Hypothesis A computational framework implementing a dynamic optimization approach that is
computationally efficient can synthesize optimum operating procedures of thermal power
plants that minimize startup and load-change times without compromising the structural
integrity of critical components.
To develop this proposed approach, the following concepts are addressed:
– Simulation models: mathematical representations capable to emulate the
dynamic behavior of a drum boiler, a combined cycle power plant, and a
cogeneration system.
– Optimization algorithm: The optimization algorithm is responsible for finding
the valve sequences that minimize the time it takes the plant to move from
an initial load to a final load. In order to do so, it interacts with the simulation
model.
– Surrogate modeling: The creation of machine learning models that minimize
the computational time for the evaluation of structural integrity of critical
components during the optimization processes. Surrogate models will be
constructed from finite element model simulations. The evaluation of
structural integrity will be based on the estimation of stresses distribution
and lifetime consumption induced by operational changes proposed by the
optimization algorithm.
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1.5 Objectives The main objective of this research is to develop a computationally efficient approach for
the synthesis of optimum operating procedures of thermal power plants which finding the
optimal control valves sequences that minimize its operating times based on techniques
of dynamic simulation, metaheuristic optimization, and surrogate modeling. The proposed
approach aims at improving the electric power system operational flexibility to address a
large-scale introduction of variable renewable energies and intermittent energy demand
scenarios. To do this, it is necessary to:
– Develop and validate dynamic simulation models of a drum boiler, combined cycle
power plant, and combined heat and power system.
– Implement an optimization algorithm for the synthesis of the startup operating
procedure of a drum boiler.
– Retrofit a cogeneration system to supply thermal energy to a continuous industrial
process with high energy demand.
– Develop and validate a finite element model of the steam generator critical
components.
– Develop and validate a computationally efficient model to estimate stresses
distribution and lifetime consumption induced by operational changes proposed by
the optimization algorithm.
– Implement an optimization algorithm for the synthesis of an optimum operating
strategy of a combined heat and power system to improve the electric power
system’s operational flexibility.
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1.6 Research methodology
This research has been developed based on an adaptation of the spiral design process
proposed by Boehm [29]. The proposed model consists of repetitive spiral-shaped cycles
that begin in the center and each loop or iteration represents a set of activities to be
developed.
The model starts from an issue identification and in each iteration, the model must
consider the research objectives, proposed approach solution alternatives,
implementation and validation of the proposed solution, as well as feedback from previous
loops. If the proposed solution does not solve the issue, improvements and functionalities
must be implemented. The proposed spiral model focuses on two control mechanisms
that measure its effectiveness, which is known as radial and angular dimensions. In the
proposed adaptation, the angular dimension represents the research progress within a
cycle, while the proposed approach complexity is quantified in the radial dimension. The
spiral model adaptation proposed is shown in Figure 1.9.
Figure 1.9. Spiral model adaptation proposed, based on [29].
Each cycle of the spiral comprises four phases: 1) problem analysis, 2) solution
proposal, 3) proposal implementation and validation, and 4) evaluation and analysis of
results. The first phase involves the problem analysis through literature review and the
33
research scope is established. In the second phase, the approach and solution
alternatives are proposed according to the scope established in phase one of the
corresponding cycle. For the third phase, one of the proposed solutions is selected and
implemented. In the last phase, a results evaluation is carried out to determine if the
research results have been achieved and the process is completed. Otherwise, the
process continues, and potential research issues are identified that were not initially
recognized, which will enrich the proposed research. The main advantage of the spiral
model lies in its iterative development, and that the improvements and functionalities can
be implemented progressively.
In this context, the spiral model allowed for an incremental development approach,
since in each phase the opportunity areas were identified, and the process was fed back
to address efficiently the current issues. The development of the research in the analysis
phase is quantified in terms of the research scope expansion, which initially focused on
finding the problem solution for the operationally critical components of thermal power
plants, and next for full thermal power plants until reaching combined heat and power
systems. For the solution proposals phase, a two-phase methodology described in [30]
was originally used, consisting of a conceptual phase and a detailed phase. The
conceptual phase focused on finding the state variables profile that minimizes the power
plant operating time without compromising the structural integrity of critical components,
while the detailed phase takes the optimal operating procedure developed in the
conceptual phase stage and generates the optimal sequence of valve operations. This
evolves into a dynamic optimization framework like the one described in [31], addressing
the problem of finding the optimal control valve sequences that minimize the startup time
using a dynamic optimization framework based on metaheuristic optimization algorithms
coupled with a dynamic simulation model. Regarding the implementation of the proposed
research approach, an interface based on the C# code was developed to connect the
power plant simulator with the framework optimization modules. Then, as a means for the
evaluation of the constraints of the dynamic simulation problem, surrogate models based
on finite element analysis were developed to estimate thermomechanical stresses in
power plant critical components. Finally, the proposed approach should be evaluated
through case studies and precise comparisons.
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1.7 Thesis outline The main contribution of this research work is the development of a computationally
efficient approach for the synthesis of optimum operating procedures of thermal power
plants which determine the optimal control valves sequences that minimize its operating
times based on techniques of dynamic simulation, metaheuristic optimization, and
surrogate modeling. Based on such an approach, the power plants must be increasing its
operational flexibility to address a large-scale introduction of variable renewable energies
and intermittent energy demand scenarios. This thesis is organized as follow:
Chapter 1 describes the problem that motivated this research work. Then the
background, problem statement, research questions, hypothesis, objectives, research
methodology, and the thesis outline are explained.
Chapter 2 presents a literature review and background of thermal power plants
modeling, simulation, and optimization to provide a context within which the contributions
of this thesis can be evaluated. Likewise, methods and techniques currently used to
evaluate the structural integrity of power plant critical components in dynamic optimization
problems are described. Finally, a review of thermal power plants retrofitting alternatives
focused on improving their operational flexibility is presented.
Chapter 3 covers the first topic of the proposed research approach in this thesis,
which focuses on the development of a framework for the synthesis of operating
procedures based on dynamic simulation and metaheuristic optimization.
Chapter 4 presents the formulation, development, and validation of the dynamic
simulation models required to implement and validate the proposed dynamic optimization
framework and the integrated approach for the synthesis of optimum operating
procedures of thermal power plants. Dynamic simulation models for a drum boiler power
plant, an existing combined cycle power plant, and a combined heat and power system
were developed and validated.
Chapter 5 describes a surrogate model based on artificial neural networks (ANN)
and finite element method (FEM) to estimate in a computationally efficient way the
structural integrity and life consumption in a thermal power plant superheater. The model
developed is compared against analytical models, as well as sub-models, and rigorous
and simplified finite-element models.
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Chapter 6 addresses the validation of the proposed integrated approach for the
synthesis of optimum operating procedures. The proposed dynamic optimization
framework is validated according to a power plant drum boiler startup optimization based
on a startup reference sequence published in the literature. Likewise, the optimal
operating procedures design of a Combined Heat and Power system based on a
retrofitting existing combined cycle power plant retrofitted, which are focused on the
efficient supply of electrical power to the system and useful thermal energy for an
industrial process is also compared with the case study used to validate the proposed
integrated approach.
Chapter 7 summarizes the accomplishments and main conclusions of this research
work, and finally, some suggestions for future works are provided.
Appendix A presents the different papers generated as part of this research work.
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2. Chapter two Literature review This chapter reviews the state of the art of the current methodologies and approaches on
modeling, simulation, and optimization related to operational flexibility.
2.1 Thermal power plants
Most of the installed power generation capacity worldwide is based on thermal power
plants. According to data from the International Energy Agency (IEA), electrical power
generation from thermal power plants in 2017 accounted for 78.9% of total world gross
electricity production, of which 74.7% corresponds to conventional power plants and the
4.2% remaining to renewable power plants [32]. World gross electricity production by
source for 2017 is shown in Figure 2.1.
Figure 2.1. World gross electricity production, by source, 2017, based on [32].
In conventional thermal power plants, electric power is generated by transforming
chemical energy stored in a primary energy source such as fossil fuels or nuclear energy
into thermal energy, which is, in turn, converted into mechanical energy, and finally
transformed into electrical energy [33]. The conversion process of thermal to mechanical
energy is carried out through power plants using steam turbines (ST) or gas turbines (GT),
whereas mechanical energy conversion into electrical power is performed by an alternator
or electric generator [34]. In the case of steam-turbine power plants, it is in the furnace of
the steam generator (boiler) where the chemical energy is converted into thermal energy,
37
while for gas-turbine power plants this process occurs in a combustion chamber [35]. The
behavior of ST and GT power plants are based on two thermodynamic cycles. The
operation of a gas turbine is described by the Brayton cycle, while the Rankine cycle
describes the thermodynamics of the water-steam cycle of the steam power plant.
Regarding operability, both technologies present advantages and drawbacks.
Both, ST and GT plants can reach up to 40% thermal efficiency. An essential difference
is that for the same power, GT installations are smaller since they have a simple design
in contrast to ST plants, which require extra equipment such as boilers, condensers, and
their auxiliary piping and equipment. However, ST plants will provide electric power in
significantly larger amounts than GT plants for turbines of the same size.
The overall efficiency of electric power plants can be increased by combining the
Brayton cycle with the Rankine cycle to recover and use the residual heat energy in hot
exhaust gases. Such process-combination is realized in combined-cycle power plants
(CCPP). Compared to ST and GT plants, CCPP’s have larger operational ranges and
efficiencies.
Over the last years, sustainable development policies related to environmental
protection and the need to improve the efficiency of electric power systems have led to
more and more efficient solutions and productivity improvements of power plants. In this
sense, solutions with high-efficiency cycles such as CCPP that provide performances
considerably higher than conventional units with efficiencies of about 60-63%, are the
trend of new liberalized markets [36]. Moreover, combined cycle technologies have lower
rates of greenhouse gas emissions [37,38]. However, most CCPP base their electric
power generation on the availability of fossil fuels such as diesel and natural gas, whose
long-term reserves costs are uncertain.
As explained in Chapter 1, thermal power plants must be operationally flexible to
meet fluctuations in demand levels, as well as to fulfill the residual load induced by non-
conventional renewable energy generation.
Therefore, one of the main challenges of electric power systems is to guarantee
high operational flexibility and reliability of the electrical grid while reducing environmental
impact and maximizing efficiency.
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Although deregulated power markets aim at a generation matrix mostly based on
renewable sources [39], in short, and medium terms, these technologies will not be able
to replace conventional thermal power plants on a massive scale. Thus, conventional
thermal power plants will continue to play a key role in the electrical power generation for
a long period. In this context, CCPP will most likely have strong growth in the coming
years due also to relatively cheap costs provided by North American shale gas.
2.2 Approaches to improve operational flexibility
Researchers have focused their attention on studying dynamic simulation and
optimization to improve flexible generation capabilities of thermal power plants.
2.2.1 CCPP Simulations models
Dynamic modeling represents one of the most powerful methods to study, evaluate, and
design operational strategies of power plants. Usually, these models are based on
differential and algebraic equations systems. Reliable models can predict accurately the
power plant dynamic behavior, enabling the development of simulators for testing and
proposing new operational strategies. Such models have been developed using different
techniques, methods, and tools.
Previous works such as those by [40-45], have shown that applications based on
theoretical and simplified models can accurately predict the power plant dynamic
behavior. For example, a simplified method based on fundamental physics laws to predict
the CCPP steam cycle under different temperatures and exhaust gases mass flow
boundary conditions was developed by Gülen and Kim [40]. Improved models have also
been developed, including those proposed by Mello [41] and Ahner [42], in which the GT
dynamic behavior is described by first-principle models based on fundamental
thermodynamic equations of mass and energy balances, based on the simplified model
of a gas turbine presented by Rowen [43]. Likewise, Shin et al. [44], proposed a model
based on the transient form of mass and energy balances for each CCPP component
combined with lumped heat capacitance and the use of a well-known correlation equation
to determine heat transfer coefficients of water and steam. Validation case studies were
39
performed using transients driven by step and sinusoidal variations in the gas turbine
load. An adapted model for the optimization process, which considers not only transient
mass and energy balance equations but also dynamic heat transfer phenomena such as
condensation, and steam turbine metal temperature profiles is described by Faille et al.
[45]. It must be noted that in most of these works, the block function diagram is used in
MATLAB or Simulink environments system modeling.
Plant-wide models have been developed based on object-oriented modeling
languages such as Modelica [46], and modeling environments such as Dymola,
OpenModelica, ASPEN Plus Dynamic, EBSILON, EcoSimPro, APROS, among others.
For example, Alobaid et al. [47,48] used ASPEN Plus Dynamic and APROS to predict the
CCPP dynamic behavior under operational conditions of partial loads, off-design and
warm startup. Simulation models were validated against a power plant's real operational
data and both simulation environments produced reliable results, but the authors
preferred APROS for its accuracy. Similarly, Wojcik and Wang [49], conducted a
feasibility study for the integration of a CCPP with an Adiabatic Compressed Air Energy
Storage (ACAES) using EBSILON® Professional software environment. Based on the
hybrid model simulations, they determined the optimal connection point for the CCGT and
ACAES models and the minimum load time to charge the ACAES system: it was found
that CAES discharging process is fully independent of CCGT process and provides an
additional 47.5% of power boost over the registered capacity of CCGT plant during peak
times.
A CCPP dynamic behavior model under real operating conditions was developed
by Benato et al [50]. The dynamic model of a three-pressure level combined cycle power
plant was developed in Dymola. In this work, simulations were carried out in steady-state
and partial load simulating also the dynamic behavior of the power plant under thermal
fatigue with the main focus onto the heat recovery steam generator. All models developed
include simplifications and assumptions such as neglecting pressure drops, friction
effects, heat loss, and similar.
The CCPP models developed by Tică et al. [51] and Hefni and Bouskela [52] were
developed and tuned with data obtained existing power plants. According to [51], the
solution of design and optimization problems based on large-scale power plant models
40
involve powerful algorithms, which impose some constraints for the model formulation.
Therefore, a method to transform a CCPP physical model in a simulation and
optimization-oriented model, which can be coupled with efficient algorithms to improve
startup performances were presented. The authors demonstrate the model consistency
and its applicability for optimization and control purposes.
In [52], the authors present the ThermoSysPro library for the OpenModelica
software for the modeling and simulation of power plants. They use this library to simulate
a dynamic model of a combined cycle power plant for a load change scenario. The model
comprises the flue gas side and the full thermo-dynamic water/steam cycle closed
through the condenser. Simulation results show that the ThermoSysPro library is
complete and robust enough for the modeling and simulation of power plants.
However, these models are limited as they can calculate ST metal temperature
evolution but cannot evaluate mechanical stresses in the steam turbine and steam
generator components.
2.2.2 CCPP operational constraints
The main barrier to the design of faster CCPP operational strategies is the presence of
thermal stress-induced fatigue damage in the steam cycle. A broad variety of research
has been done to find those components that are more prone to failure due to severe
changes in operating conditions. In this context, the work carried out by Shirakawa et al.
[53], Lind et al. [54], Alobaid et al. [55], Kim et al. [56] and Mertens et al. [57] consider the
high-pressure drum as the most critical component of the power plant. Meanwhile, the
work of Alobaid et al. [58], Mirandola et al. [59], Farragher et al. [60], Hentschel et al. [61],
Taler et al. [62] and Angerer et al. [63] identify the high-pressure superheater header as
a component even more critical than the high-pressure drum. Likewise, Shirakawa et al.
[53], Casella et al. [64], Spelling et al. [65], Born et al. [66], Moroz et al [67] and Ji et al.
[68] consider the steam turbines as the most critical component.
An accurate and computationally efficient evaluation of stress levels and life
consumption in critical components plays a critical role in the optimal design of CCPP
operating procedures. In the literature, different methods and techniques have been
developed to quantify the thermomechanical stress in the critical components under
41
dynamic optimization and cyclic operation scenarios. For example, Moroz et al. [67]
propose an integrated approach for steam turbine components thermo-structural analysis
and lifetime prediction. Thermal boundary conditions were established from convective
heat transfer coefficients in the rotor and casing surfaces and calculated based on heat
transfer theory and general equations such as Dittus-Boelter's. Likewise, three
dimensional transient thermal and structural Finite Element Models (FEM) for the casing
and axisymmetric bidimensional FEM for steam turbine rotors were developed. They pay
special attention to some of the key factors that influence the accuracy of thermal stress
prediction, specifically, on the thermal boundary conditions, the definition of thermal
zones and thermal contacts, as well as the mesh quality and refinement in critical zones
with high potential of stress concentration to crack initiation. They consider that the high
and intermediate pressure rotor is the critical component that determines the power plant
structural integrity and use the Low Cycle Fatigue (LCF) criterion to determine useful life.
The model input data are the pressure and temperature profiles measured during a cold
startup test of a 30 MW steam turbine. Dettori et al. [69] proposed a Nonlinear Model
Predictive Control (MPC) as a strategy for the control of steam turbines rotor thermal
stresses. Their approach focused on controlling the convective heat transfer coefficient
and boiler steam reference temperature. Since the calculation of thermal stress must be
fast enough, they use a simplified stress model based on the thermal transient
thermoelastic behavior of steam turbine rotors similar to that developed by Nakai et al
[70]. This model considers the rotor as an axially infinite cylinder that takes into account
local changes in material properties as a function of temperature and axial temperature
variations are negligible. Their stress model was validated against a steam turbine FEA
model. Ji et al [68] presented a machine-learning approach for speeding up the
calculation of thermal stresses for minimizing the startup time. Their approach worked by
constraining the maximum Von Mises stress of five critical zones of the rotor where the
greatest stress concentrations are located. The rotor was considered a homogeneous,
isotropic, and non-heat source object in the thermal transient analysis. Due to their
geometrical and structural characteristics, a 2-D axisymmetric analysis is enough to
determine the rotor behavior under mechanical conditions. Some rotor geometric details
were simplified to save computational time, keeping the accuracy of the model. The
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convective heat transfer coefficients were determined using the Haqi- Nangong model
[71]. Based on FEM simulations results, they used a support vector machine model and
particle swarm optimization algorithm to find the optimal temperature ramp rate in the cold
startup process.
On the other hand, Weglowski et al. [72] present the stress evaluation of drum
boiler water walls during the startup process. To determine the circumferential
temperature distributions along the drum boiler wall, temperature measurements at
selected spatial points were considered. They assumed a two-dimensional temperature
field across the drum length; thus, the drum pipe cross-section was only considered.
Because of the large wall thickness of the pressure component, the thermomechanical
stress evaluation was carried out using a three-dimensional model. Their 3D Finite
element model considers an insulated outer surface to minimize the heat loss to
surroundings; it was also assumed an asymmetrical temperature field in the drum cross-
section, thus evaluating only half of the tube. According to their results, it is concluded
that stress profiles for the water wall drum boiler during this startup process are lower
than the material yield strength. In the same way, Bracco et al. [73] develop a model for
the calculation of thermal and mechanical stresses which can also be used for the
estimation of the low-cycle fatigue damage of high-pressure steam drums in a combined
cycle power plant. It was proposed a procedure to estimate the useful life of steam drums
under cyclic operation schemes. The simulation model evaluates the steam drum life
reduction according to the analytical method described in EN 13445 Standard, assuming
uniaxial equivalent stress according to the rainflow cycle counting method4 reported by
the ASTM E 1049 Standard. The proposed model is characterized by low computation
times and high reliability and was tested against a power plant experimental data.
Pang et al. [74] present a study focused on evaluating the temperature changes in
boiler water-cooled wall pipes during fluctuating operation. They consider temperature
distributions and differences among parallel tubes along four side water-cooled walls.
They developed a two-dimensional mathematical model based on ANSYS software to
determine the cyclic thermal stresses and identify the maximum stress positions of the
4 The rainflow-counting algorithm is used in the analysis of fatigue data in order to reduce a spectrum of varying stress into an equivalent set of simple stress reversals [75]. The original algorithm was developed by Tatsuo Endo and M. Matsuishi in 1968 [76].
43
water-cooled walls was proposed. According to their results, the stresses caused by the
cyclic operation are higher than in other operation schemes, and they conclude that the
boiler operational load must be limited by the furnace combustion uniformity and the two-
phase flow distribution inside the intermediate header before the vertical water wall.
Benato et al. [77] propose a procedure to predict the power plant dynamic behavior during
load variations, as well as the identification of the higher-stress components with which
they estimate the equipment lifetime reduction. This research aims to investigate the
relationship between plant operation and its components lifetime reduction. They propose
a Lifetime Estimation (LTE) procedure, which is composed of a plant dynamic simulator
(PDS) and a Fatigue Life Calculation tool (FLC). The PDS determines the profiles of main
thermodynamic parameters (mass flow rates, temperatures, and pressures), and using
this procedure it is analytically calculated the thermomechanical stress in critical
components. The stresses so evaluated become the input for the estimation of the
components residual life using the FLC tool, which is based on the EN13445 Standard.
This procedure is applicable for the lifetime estimation of power plant thick-walled
pressure vessels such as the superheater and drum. It was so concluded that this
procedure is much faster in comparison with a finite element analysis tool. Farragher et
al [29] propose a procedure to quantify the thermomechanical fatigue of a subcritical
power plant outlet header under realistic loading conditions based on the finite element
method. The thermal model that simulates the power plant cycle involves the convective
heat transfer coefficients calculation. Natural convection is modeled on the header
external surfaces, while forced steam convection is modeled on the header internal
surfaces. Transient heat transfer, with temperature-dependent conductivity and specific
heat data, is modeled through the header walls. A global finite element sub-modeling
technique is employed to deliver an efficient but accurate solution to this complex three-
dimensional thermo-mechanical problem5. To this end, a detailed mesh refinement study
has been also conducted to establish a converged sub-model mesh for the analysis. The
Ostergren parameter was then the chosen fatigue indicator parameter to predict the
location, orientation, and life for crack initiation under multiaxial conditions. The results
5 A key challenge in the thermo-mechanical analysis of power plant components is the need to capture complex geometries, including stress concentrations and to provide an accurate representation of time-dependent and possibly non-linear thermal and mechanical response, in practical computation times
44
show that transient stresses are effectively more detrimental; the outside surface cracking
is predicted to occur about 60% later than inside surface cracking. Similarly, Taler et al.
[78] developed a transient mathematical model focused on power plant steam generator
cold startup optimization with an emphasis on the maximum allowable thermal stresses
of boiler thick wall devices. This study assumes that permissible heating rates of thick
boiler elements are usually determined by the boiler manufacturers, which are usually
very small, and the startup of the boiler takes a long time. Likewise, these heating rates
can be calculated using the European Standard EN-12952-3; however, accurate
structural analysis using the finite element method, shows that the allowable stresses at
the hole edges are exceeded by the heating rates calculated according to this standard.
In this context, a new method is proposed [78] for determining the optimum temperature
and pressure runs during boiler startups and shutdowns. The proposed heating of the
pressure elements is conducted so that the circumferential stress caused by pressure
and fluid temperature variations at the edge of the opening at the point of stress
concentration, do not exceed the allowable value. Optimum fluid temperature changes in
the form of a simple time function are assumed and it is possible to increase the fluid
temperature stepwise at the beginning of the heating process. the fluid temperature can
be then increased with a pressure-dependent rate. The proposed method shortens the
duration of the boiler startup according to the final findings [78].
Okrajni and Twardawa [79] have addressed the issue of the modeling of strains
and stresses resulting from heating and cooling processes of the thermal power plants
superheater header under mechanical and thermal loading. The determination of time-
variable temperature fields was conducted assuming that the heat transfer coefficient on
the inner surface of the header depends on the steam flow rate, steam pressure, and
temperature; since on outer surface of the header the heat exchange is less intensive, a
constant value heat transfer coefficient has been used. Computer superheater header
FEM modeling has been developed in order to determine the temperature strain and
stress fields. Stress distributions calculations indicate concentration areas in the vicinity
of the holes6. In order to determine the intensity of the damage accumulation process, a
6 For the power plant thick-walled pressure vessels such as the superheater and drum under operational conditions, the cracks appear in the vicinity of the holes.
45
local analysis of the relationships between temperatures, stress, and mechanical strain
has been developed. Yasniy et al. [80] carried out a study of the residual lifetime
assessment of thermal power plant superheater header based on the finite element
method. The ligaments between the holes of nozzles supplying superheated steam are
the most prone zones to operational damage and defects according to their findings.
Lifetime is evaluated on fluctuations of temperature under the quasi-static operational
regime. The FE model was developed using ANSYS commercial software and the
modeling involved solving an elastic three-dimensional problem. Their finite element
mesh was refined in the vicinity of critical zones while internal surfaces of the headers
cylinder, holes and nozzles were loaded with pressure and temperature. The transient
thermal analysis results were transferred to the static structural module: the stress state
was thus calculated taking into account the non-uniform thermal expansion of the material
through the thickness of the header wall and the non-linearity of physical and mechanical
properties of the material. In addition to the temperature effect, the internal surfaces of
the cylinder, holes, and nozzles were loaded with operational steam pressure. The
residual durability of the superheater header was then evaluated considering an existing
defect along the central hole of the superheater and assuming crack growth according to
the well-known Paris law.
2.2.3 CCPP retrofitting
One way to increase the electric power system operability is by retrofitting existing power
plants through cogeneration systems or combined heat and power systems (CHP) thus
generating electricity and using heat that would be otherwise, wasted to produce thermal
energy for residential or industrial purposes. Likewise, capabilities to adjust demand to
respond to periods of supply shortages and over-generation are both incorporated into
the system. One advantage of this approach is that it can reduce emissions and
operational costs, as well as increase power system reliability and thermodynamic
efficiencies. For example, unused heat in an electrical power plant can also supply
thermal energy for industrial processes, heating, cooling, or be combined with hydrogen
production for electrical vehicle mobility. Another benefit of this approach is that
operationally flexible turbines such as gas turbines are widely used for CHP systems. For
46
example, in the US, gas turbines account for 52 GW of installed CHP capacity, which
represents 64% of the total installed CHP capacity in the county [81]. It is worth
mentioning that more than 80% of CHP systems based on gas turbines are combined
cycle power plants improving the basic gas-turbine cycle.
Studies have been published related to the design and optimization of
cogeneration systems in the context of District Heating and Cooling (DHC), mainly for
countries with long heating periods and growing cooling requirements during summer
seasons. Sdringola et al. [82] proposed a management profile, enhancing both the
operational and economic parameters of a small CHP plant located within a research
facility in Italy. The CHP plant was designed to supply electricity, heating, and cooling
through a district network based on monitored consumption of electricity, heating, and
cooling, constraining the energy fluxes. Rolfsman [83] presented an operational
performance study of the district heating system for the city of Linköping in Sweden. In
this study both electricity and heat energy for the city are provided by a CHP plant. The
major focus of this study [83] was to maximize electricity production during periods of high
electricity prices. The author proposed storing heat, both in a hot-water accumulator at
the CHP plant and in dedicated storage in the building stock. The case study was
developed using a mixed-integer linear programming model.
In addition to the above, Rakopoulos et al. [84] studied the technical, economic,
and environmental performances of different configurations of CHP systems for use in
district heating (DH) networks based on lignite-fired power plants. For summer and winter
operational modes, the thermal cycle and plant efficiency were computed by using a
specific thermal cycle calculation tool [84]. Likewise, electricity and thermal energy
generation costs, as well as the net annual profit was evaluated. The performed
calculations showed an important increase in electrical and thermal efficiencies in the pre-
dried lignite firing case as well as considerable fuel savings and CO2 emissions
reductions. Therefore, greater competitiveness of the CHP system is to be expected [84].
Other researchers studied the coupling of the other generation technologies in
CHP integrated systems. In this context, the work of Värri et al. [85] assessed the ability
of nuclear power plants to be coupled with thermal energy systems in the European
heating sector. They evaluated the sustainability and cost-effectiveness of small modular
47
nuclear reactors (SMR) for district heating through literature review and scenario
modeling. The case study considered a 300 MW asset for a new district heating capacity
in Helsinki to be installed by 2030 either as a CHP plant or as a heat-only boiler. The
results showed that these technologies seem promising and could be profitable in a
modular nuclear heat-only boiler, while a modular nuclear CHP plant still has a relevant
uncertainty around its costs and possible deployability [85].
Looking at industrial applications, Gambini et al. [86] presented a techno-economic
feasibility analysis of high-efficiency CHP plants to be coupled with the Italian paper
industry. Danon et al. [87] presented a techno-economic analysis of a CHP plant based
on wood residues from the Serbian wood industry. The cost of electricity generation was
assessed using five different kinds of CHP technology suitable for the wood industry.
Ahmadi et al. [88] presented a feasibility study of a combined heat and power
(CHP) plant in a paper mill installed in Iran. Exergy efficiency, total cost rate of the system
products, and CO2 emission of the whole plant were the main performance indicators
considered for the feasibility evaluation of the proposed design of the cogeneration plant.
In the mining industry, Jannesari et al. [89] presented a techno-economic evaluation of a
solar-assisted heating system to provide thermal energy to the electrowinning process of
the Sarcheshmeh copper complex installed in Iran. In this research, both single-objective
and multi-objective genetic algorithms were implemented for the economic optimization
of the collector arrangement, sizes of storage tanks, and solar farms. In the study [89],
heat transfer fluid behavior, collector technology, and orientation effects were considered.
Based on the results, the implementation of the design led to a reduction of roughly 970
tons of CO2 emissions per year.
2.2.4 CCPP operational optimization
According to data from the International Energy Agency [90], in the short term to medium
term, optimized operations are to be considered as the most effective solution to deliver
power system operational flexibility. This approach can be applied to conventional plants
as well as future technologies based on energy storage. Specifically, studies on flexible
generation in conventional thermal power plants have been reported in previous works
such as those by Kubik et al. [91], Hentschel, and Spliethoff [25]. Gonzalez-Salazar et al.
48
[28] concluded that the most suitable power plants to provide operational flexibility to the
electric power system are the simple gas turbine cycle, high-efficiency coal-fired, and
combined cycle power plants. Likewise, they identified that the development trend of
these power plants is focused on operational improvement in terms of increasing ramp
rates, decreasing minimum power load, and the development of the improvements of
cyclic operational capabilities. In this context, research such as that developed by Casella
et al. [64], Almodarra et al. [92], Anisimov et al. [93], Rossi et al. [94], Ji et al. [68], and
Liu and Karimi [20] addressed the flexible generation challenge through the conventional
thermal power plants operating profiles' optimization. On the other hand, as a first step
for the analysis of the whole power plant and using a hierarchical optimization strategy,
the works of Franke et al. [95], El-Guindy et al. [96], Elshafei et al. [97], Belkhir et al. [98],
and Zhang et al. [99] proposed to manage the operation of the power plant using a
process level approach.
Researchers have focused their attention on studying dynamic simulation and
optimization of steam generators to improve the flexible generation capabilities of thermal
power plants. Specifically, previous works [64, 68, 93, 94] focus on the study of power
plant transient behavior as a means to propose and design optimal operational strategies.
To that end, dynamic simulation models were developed based on mass, momentum,
and energy conservation laws.
Early simulation models of power plants steam generators were based on a simple
nonlinear model of a boiler turbine unit. Some of these models were proposed by Astrom
and Euckland [100]. Astrom and Bell [101] improved the linear model developed by
Astrom and Euckland and validated it with experimental data, finding that the model was
capable of capturing the dynamical behavior of the system. Later, Peet and Leung [102]
proposed a dynamic simulation model to design a drum boiler based on the requirements
of a conventional thermal power plant’s operation to achieve flexible and economic
production of steam. Subsequently, Bell and Astrom [103] developed a nonlinear model
of a drum boiler based on the principles of their initial model, and its transient performance
was validated against real power plant data. In the control arena, Flynn and O’Malley
[104] developed a drum boiler dynamic simulation model and used it in the study and
design of a new control strategy to meet the operational requirements of a large fossil fuel
49
power plant. Over the years, drum boiler models grew in complexity and accuracy, mainly
by replacing empirical coefficients with real operating parameters. A commonly cited
model is that of Astrom and Bell [105], which was a nonlinear dynamic model in which the
downcomer, riser, and drum dynamic behaviors were based on a global balance of
conservation laws and required few physical parameters to have a simple and robust
system.
Subsequently, Wen and Ydstie [106], El-Guindy et al. [96], Elshafei et al. [97],
Belkhir et al. [98], and Zhang et al. [99] developed simulation models based on the
theoretical model proposed by [105], using advanced modeling and simulation
techniques.
Regarding the operation of power plants, several works have been reported in the
literature that dealt with the optimization of steam generation from a process point of view.
Franke et al. [95] developed a nonlinear dynamic model of a drum boiler based on the
Modelica language using the fluid libraries [107]. The model had three control inputs in
terms of feedwater flow rate, heat supply, and steam outlet. A dynamic optimization
problem using sequential quadratic programming (SQP) algorithm was solved. Using this
approach, the startup time could be reduced by 30%. Kruger et al. [108] proposed a
quadratic programming optimization approach to determine the optimal values of steam
pressure and steam temperature in a startup process. The model took into account hard
constraints such as control bounds and stress levels for the drum and header: the
proposed optimization model is capable of minimizing both fuel consumption and startup
time. Li et al. [109] developed a drum boiler startup simulation program that focused on
reducing the operational time and minimizing fuel consumption during startup or
shutdown scenarios. A distributed parameter method was used to simulate the heat
transfer process in the waterwalls, superheater, reheater, and the economizer, while heat
transfer in the drum and the downcomer was simulated by lumped parameter analysis.
Moreover, Belkhir et al. [98] minimize the startup time of a steam generator. The proposed
startup strategy focused on achieving reference state variables in terms of steam mass
flow rate and the pressure inside the drum to fulfill the steam requirements in the power
train. The startup process was formulated as an optimal control problem that minimized
a quadratic objective function under physical and operational constraints. The physical
50
constraints were related to the structural integrity of thick-walled components due to
higher thermal stresses. The drum boiler model was developed in the commercial
Modelica environment Dymola using the available fluid and thermal libraries. The
optimization problem was solved by combining a framework developed on the JModelica
environment and interior point optimizer algorithm (IPOPT). The results were compared
against a classical startup strategy, and the optimized profiles reached desired states in
a shorter time without violating the operational and physical constraints. Zhang et al. [99]
presented a numerical investigation on the dynamic analysis of the steam and water
system of the natural circulation boiler developed in the environment of
MATLAB/Simulink. A boiler modeling based on the Astrom–Bell model with specific
parameters to simulate the dynamic analysis of the steam water system was proposed.
The model assumed that steam was saturated along with the whole evaporating system.
This model was solved using the ode45 algorithm, which is based on the fourth-order
Runge–Kutta, and Dormand–Prince methods. The boiler startup was formulated to get a
better curve of the startup in order to save water and fuel. The input parameters were
heat flow, the mass flow rate of steam, and the mass flow rate of feedwater, which were
changing with time. Finally, a procedure for a cold startup was developed obtaining a cold
startup curve that could be used as a reference for practical production.
Albanesi et al. [110] also carried out a combined cycle power plant startup
optimization using a model-based approach. The simulation model considers the section
between the gas turbine and the high-pressure steam turbine, which includes elements
such as the gas turbine, heat exchangers, evaporator, gas turbine bypass valve, steam
turbine, and steam piping pressure drops. The control variables of the optimization
problem were the gas turbine load variation, the steam turbine governor valve opening,
and the steam turbine acceleration, while the objective function was set to minimize the
power plant startup time. The main optimization constraint was related to lifetime
consumption in the steam header and the steam turbine rotor. To solve the optimization
problem, a Sequential Quadratic Program (SQP) solver implemented in the C
programming language was used. Ji et al. [68] have presented a study based on finite
element simulations, support vector machine algorithm (SVM), and the particle swarm
optimization (PSO) algorithm to minimize the steam turbine startup time and constraint
51
the turbine rotor stresses. Five segments with different main steam temperature rise rates
were identified leading to twelve cold-startup profiles to be used. So, the startup problem
was formulated as a function optimization problem with constraints. The optimization
problem was formulated so as to minimize the steam turbine startup profile, at the same
time that the equivalent Von Mises stress remains within the limit strength of the rotor
material. In this study, SVM was used to establish the regression model between the main
steam temperature parameters and the maximum Von Mises stress of the steam turbine
rotor based on the SVM toolbox in Matlab. A genetic algorithm was applied to search the
optimal parameters of the SVM algorithm to improve the stability and accuracy of the
regression model. The main steam temperature rise rate optimal solution was found out
by using PSO combine with the SVR model. Their results show that startup time can be
shortened by nearly about 17% without exceeding permitted Von Mises stress.
Liu and Karimi [20] proposed a simulation-based optimization approach for finding
a gas turbine combined cycle power plant optimal operating strategy that maximizes the
overall plant efficiency for any partial load operation. To obtain the best operating
strategy, the used optimization considers both power plant cycles (Brayton and Rankine).
The methodology was based on a coupled system of a power plant simulator in
GateCycle7 and a Particle Swarm Optimization (PSO) algorithm implemented in Matlab.
To maximize the power plant efficiency at a given part-load, their optimization strategy
considers as the optimization variables the inlet guide vane (IGV) angle, fuel flow, cooling
airflow, and four water flows (desuperheaters, recirculation, and bypass) in the Heat
Recovery Steam Generator (HRSG). The operational constraints during optimization
ensured that the metal temperature on each turbine blade remains below the design metal
temperature and the high-pressure steam and reheat steam temperatures are kept under
their design values. This proposed strategy increases plant efficiency by about 2.63%.
Yoshida et al. [111] proposed an optimization method to solve multi-objective
problems involving the minimization of startup time, life consumption, and fuel gas
consumption in a gas turbine combined cycle power plant. The optimization procedure
was implemented as an optimization layer coupled with a dynamic simulator. The
7 GateCycle is a software used to model the steady-state design and off-design performance of thermal power plants. http://www.wyattllc.com/GateCycle/GateCycle.html.
52
optimization searched for optimum parameters that are associated with startup profiles
such as the gas turbine load ramp rates and flue gas flow. The objective functions are
formulated based on the reduced fuel gas consumption and life consumption of
components. In this paper, the NSGA-II (Non-dominated Sorting Genetic Algorithm) was
employed to solve the multi-objective optimization problem. To validate the dynamic
simulator, the results were compared with existing plant operational data. The proposed
method generated startup curves on the Pareto-front (ref?) representing the best trade-
off between the fuel gas consumption in the gas turbine and the thermal stress in the
steam turbine rotor. The results showed that this methodology is well capable to optimize
the startup curves of the power plant.
53
3. Chapter three Dynamic optimization framework 3.1 Introduction
As explained in the literature review, much research has been done on optimizing the
startup processes of the drum boiler and CCPP to improve the operational capabilities of
thermal power plants. However, these works have limited applicability since they were
solutions to specific problems. For instance, in many cases, the simulation model was
embedded within the optimization tool and it was not possible to scale them for more
complex problems. Other works propose approaches using commercial tools for the
coupling of a simulation-optimization integral system. The drawback is that these tools
operate as black boxes, with limited information about the modeling assumptions. A third
group of contributions, despite taking into account thermal stress evaluation, seek to
minimize startup times regardless of how the plant must be operated to achieve a given
goal state.
Unlike previous works, this research addresses the problem as a dynamic
optimization problem to synthesize, in an integral way, the optimal operating procedures.
The proposed approach produces operating procedures that minimize the time needed
to take the power plant from an initial state to any goal state along with their corresponding
sequence of control valves operations without compromising the structural integrity of
critical plant components. In this context, a dynamic optimization framework based on
metaheuristic optimization algorithms coupled with dynamic simulation models is
proposed. This framework is based on the implementation of a metaheuristic optimization
algorithm (such as a genetic algorithm) coupled with a scalable dynamic simulation
model, using the modeling and simulation environment OpenModelica. An open interface
based on the C# code is developed in order to connect the dynamic simulator with the
optimization module.
54
The optimization problem for the synthesis of optimum operating procedure is
formulated as follows:
𝑀𝑖𝑛 𝛼 ∑𝑑𝑡
𝑡𝑓
𝑡0
+ 𝛽‖𝑥𝑓 − 𝑥(𝑡𝑓)‖
Subject to:
𝑓(𝑥(𝑡), �̇�(𝑡), 𝑢(𝑡)) = 0
𝑥(𝑡0) = 𝑥0 𝑔(𝑥) ≤ 0 𝑢(𝑡) ∈ 𝑈 𝑈 = [𝑢1, 𝑢2, … , 𝑢𝑛]
𝑇
where ∑ 𝑑𝑡𝑡𝑓𝑡0
is the time needed to take the system from an initial state to a goal state;
𝑥(𝑡) represents the state that characterizes the evolution of the system through time; 𝑥0
and 𝑥𝑓 are vectors that represent the system initial state and final state respectively; 𝑢(𝑡)
is a vector that represents a set of operations performed at time 𝑡; 𝑓(𝑥(𝑡), �̇�(𝑡), 𝑢(𝑡)) are
a set of equations describing the process behavior, 𝑔(𝑥) a vector of inequalities
representing a process, structural integrity, and other constraints; 𝑈 represents a set of
predetermined operations such as specific valve positions; and 𝛼 and 𝛽 are parameters
that depend of the problem and guide the solution to find the optimal. When 𝛼 = 0 the
problem is reduced to finding the sequence of operations that result in a feasible trajectory
but not necessarily optimum. A feasible solution is one that achieves the goal without
violating any constraints.
3.2 Proposed approach
3.2.1 System architecture
The system architecture of the framework is shown in Figure 3.1.
Figure 3.1. Implementation of the framework.
56
This framework consists of four modules: simulator, optimizer, solution generator,
and evaluator. Likewise, an interface based on C# code was developed in order to
connect the simulator module with the framework optimization modules.
The simulator is used to predict the dynamic behavior of the system through the
solution of models made of differential and algebraic equations systems. Each operating
procedure created by the solution generator is sent to the simulator in order to determine
the state variables profiles that describe the behavior of the system, which will be used in
the evaluator module. The simulation models were developed using the modeling and
simulation environment OpenModelica.
To solve the dynamic optimization problem, the optimizer executes a metaheuristic
algorithm and interacts with the solution generator, submitting requests for new solutions.
The main role of the solution generator is to create an individual, which represents
an operation procedure. Each individual is composed of three vectors, which contain
information about the control valve positions, the valve positions times, and the number
of repetitions of each valve position. For each individual that is generated, the solution
generator creates a file that contains the operating sequences for each control valve of
the process.
Then, the C# interface translates this file to the Modelica code and merges it with
the Modelica.mo file of the simulator. The Modelica.mos file contains the simulator script
and has the function of running the simulations using the OpenModelica OMC compiler.
The simulation results file .mat through the C# interface is sent to the evaluator module
in order to calculate the objective function and evaluates the constraints. This information
is then passed to the solution generator to continue with the optimization algorithm until
it achieves a given stop criteria. Both the solution generator and the evaluator are
implemented in C#.
3.2.2 Optimization algorithms
To the optimum operating procedures, two metaheuristic optimization algorithms were
implemented, namely, a micro genetic algorithm (mGA) based on Batres [112] and a
hybrid algorithm based on simulated annealing and tabu search.
57
3.2.2.1 Micro Genetic Algorithm (mGA)
Just like any traditional genetic algorithm (GA), a micro genetic algorithm (mGA) solves
optimization problems with or without constraints using a natural selection process that
emulates biological evolution. However, micro genetic algorithms are characterized by
small populations of individuals. Each individual represents a solution (an operating
procedure). A three-chromosome configuration is used so as to avoid the need of a
variable-length chromosome such as proposed by Batres [112].
The flow diagram of the mGA is shown in Figure 3.2. It consists of an outer loop
and an inner loop. The outer loop consists of creating a new random population,
transferring the best individual from the inner loop and restarting the inner loop. The
amount of individuals that formed the random population is a parameter of the algorithm.
The traditional genetic algorithm is used as an inner loop, consisting of the evaluation of
the fitness of each member of the population, the selection of parent chromosomes, the
generation of a new population by means of the crossover and mutation operations, and
the separation of the best-fit individual after convergence.
Figure 3.2. Operation diagram of the mGA.
Here, the outer-loop iteration is called an epoch, and every cycle of the inner loop
is called a generation. The following is a detailed explanation of each of the steps in the
mGA.
58
The first step consists of the generation of a random population. In this step, a
random group of individuals is generated. In Figure 3.3, an illustration of a random
generated population is shown.
Figure 3.3. Example of a random population of four individuals.
Use crossover and mutation operators to generate a new population: The
proposed mGA implemented two genetic operators, which are controlled by the crossover
probability and the mutation probability, respectively. The crossover probability is a
parameter that determines how often the crossover will be performed. Similarly, the
mutation probability determines the frequency in which a mutation occurs. Firstly, the
crossover operator selects two individuals (mom and dad individuals). These individuals
are selected based on the roulette-wheel scheme [113]. Then, it selects two random
genes in the chromosomes (which cannot be the first or the last gene). Then, the mom
and dad individuals are split by the selected genes into three pieces. Then, from the
pieces of the mom and dad individuals, two new individuals are formed (daughter and
son). Son and daughter individuals have the middle part of mom and dad, respectively.
Then, the left and right part of the dad individual becomes the left and right part of the
daughter individual, and the left and right part of the mom individual becomes the left and
right part of the son individual. In Figure 3.4, a graphical representation of this process is
presented.
59
Figure 3.4. Graphical representation of the crossover genetic operator in the mGA.
When a mutation occurs, mGA first selects one individual. This individual is also
selected by the roulette-wheel scheme [113]. Then, it selects two random genes in the
chromosomes (which cannot be a gene with the repetitions = 0). Then, the selected genes
inside the individuals are swapped. In Figure 3.5, a graphical representation of this
process is presented.
Figure 3.5. Graphical representation of the crossover genetic operator in the mGA.
In Figure 3.6, an example is given to illustrate how the population in Figure 3.5 was
modified using the crossover and mutation operators.
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Figure 3.6. The new population after the crossover and mutation operators.
In the fitness evaluation step, every member (individual) of the population is
evaluated using a fitness function. The fitness function is inversely proportional to the
objective function. In Figure 3.7, an illustration of the fitness result associated with each
member of the population is shown.
Figure 3.7. An example of the fitness associated with each member of the population.
After convergence of the inner loop, the individual with the highest fitness function
is labeled as the best individual. In Figure 3.8, an illustration of how the best individual is
selected is shown.
61
Figure 3.8. An example of the selection of the best individual of the population.
After the first iteration of the inner loop, a new population is created randomly and
the best individual is inserted into it. In Figure 3.9, an illustration of how the best individual
is inserted into the new random population is shown.
Figure 3.9. An example of the selection of the best individual of the population.
Each individual is represented as an ordered list of operations. As in other genetic
algorithms, each candidate solution in the population (an individual) is represented by a
data structure called the chromosome. However, this research proposes a three-
chromosome data structure. The first chromosome represents the sequence of valve
62
actions. The second chromosome represents the action duration, and the third
chromosome represents the number of times that the same action is repeated.
The action duration is the execution time associated with each action for which
valve positions are kept unchanged. The repetition parameter shows the number of times
that action is carried out. Both the valve position and the action durations are discretized.
An indexed list was created containing the possible combinations between valve
openings and action durations. Figure 3.10 shows an example of an individual
represented by the proposed three chromosome scheme.
Figure 3.10. An example of the selection of the best individual of the population.
3.2.2.2 SATAS Hybrid Algorithm
SATAS is a hybrid algorithm that combines the elements of two well-known metaheuristic
algorithms: Simulated Annealing and Tabu Search. The SATAS Hybrid Algorithm aims to
improve the computational efficiency of each algorithm. To improve the performance of
the SATAS hybrid algorithm, the search zone in the cooling element from the simulated
annealing algorithm and the efficient computational performance provided from the tabu
search algorithm memory structures are used.
In order to improve the SATAS hybrid optimization algorithm convergence, and as
a basis for finding an optimal solution, the generation of a feasible seed is proposed as a
reference solution. In this context, the operating scheme of the SATAS hybrid algorithm
is composed of two steps as shown in Figure 3.11.
Figure 3.11. Operating scheme of the SATAS hybrid optimization.
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3.2.2.2.1 Seeding generation
Usually, to solve a dynamic optimization problem based on metaheuristic optimization
algorithms, a random initial solution is used. In this sense, the SATAS hybrid algorithm
proposes the generation of a reference feasible seed which is based on the operating
scheme described in Figure 3.12.
Figure 3.12. Operation diagram of the seed generation algorithm.
The first step consists in the generation of a random procedure using the three-
chromosomes structure established previously. This procedure can have any of the
actions, times and repetitions established by the problem. Figure 3.13 shows an example
of two procedure with the structure of three chromosomes, with nine genes, generated
randomly. We can observe that both have random values, but these values are in the
same range of the discrete values of a specific problem.
Figure 3.13. Randomly generated procedures.
64
Once the first solution is generated, it is evaluated in the simulation model through
the communication interface and its feasibility is analyzed. A solution is considered fully
feasible if it reaches the objective set by the problem without violating any restrictions,
whether or not it is an optimal solution.
With this evaluation, a scale is generated to determine how close to being feasible
a solution is. On this scale, one means a feasible solution, and five means an unfeasible
solution.
Based on this scale, a series of mutations will be made to the operation procedure.
The relationship between the scale and the number of mutations can be seen in Table
3.1. Using this relationship, it is possible to generate increasingly feasible solutions, and
the closer the operation procedure is to the feasibility the lower the mutations are
performed on it so good results do not suffer large changes.
Table 3.1. Relation between feasibility scale and number of mutations in the operating procedure for an example of 9 genes.
Feasible scale Number of mutations
1 0 2 1 3 2 4 3 5 4
A mutation is the generation of a new procedure based on the previous solution.
The mutation consists of taking the previous solution and randomly changing one of the
genes of each chromosome to another gene of the same population (action, time and
repetition). Figure 4.14 shows how the process works from 1 to 4 mutations in an
individual of nine genes.
65
Figure 3.14. Mutation process from one to four mutations.
The new solution has to be reevaluated to assign a value on the feasibility scale.
Hence, you enter a loop that generates mutations on the solutions until you get total
feasibility. At this point, the feasible solution is maintained, and it goes on to the next
process of the optimization method.
It is important to mention that it is possible to start the process with an already
feasible solution, therefore, the algorithm will assign a scale of feasible solution (1) and
go to the next process without making mutations
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3.2.2.2.2 Optimization algorithm
This step represents the optimization process of the feasible procedure, which is shown
in Figure 3.15. The final result of this process should be the solution optimized by the
optimization algorithm.
Figure 3.15. Optimization process operation.
The SATAS hybrid optimization algorithm is considered a metaheuristic hybrid
algorithm because it shares characteristics of two base metaheuristic algorithms known
as simulated annealing algorithm and tabu search algorithm.
The main component of the simulated annealing algorithm is the “cooling” element
that allows the selection of new “worse” solutions at the beginning of the iterative process
in order to avoid stagnating in local optimum, this is known as the “hot” part of the process.
But as the algorithm progresses, its "cools" so the probability of selecting "worse"
solutions decreases and only moves if the result improves.
The use of memory structures was considered the main element of the tabu search
algorithm. These are data strings that contain information of previously evaluated
solutions. These data structures have two main applications. The first application is to
avoid search stagnation between solutions that have already been evaluated and the
second is to improve the computational efficiency of the algorithm by recognizing and
avoiding evaluation in the simulation model of previously analyzed solutions. The flow
chart of the SATAS hybrid algorithm is shown in Figure 3.16.
67
Figure 3.16. Operation diagram of the SATAS hybrid optimization algorithm.
The first step is to generate a neighbor solution of the feasible solution that is
delivered from the process of generating seed. A neighbor solution is a solution close to
the original solution. In this case, it is considered a neighbor the solutions with a mutation
with respect to the actual solution. Figure 3.17 shows examples of neighbor solutions for
the three-chromosomes individual with nine genes.
Figure 3.17. Example of five neighbors (one mutation) from an actual solution.
By selecting and evaluating the first neighbor, that neighbor becomes part of the
tabu list, and the memory structures are generated. Thus, each new solution will be
analyzed to verify if it has been previously evaluated, and if so, its evaluation will be
avoided, and a new neighbor will be generated. This ensures to perform search in new
areas and helps to avoid stagnation. Another benefit of memory structure is to avoid
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simulating sequences that have already been simulated, this is very important for
computational efficiency because depending on the complexity of the system and the time
required to carry out each simulation.
The next step is the analysis of the neighbor solution. First, it is verified if the
neighbor solution is feasible. Then, the neighbor solution is analyzed if this neighbor
solution is worse or better than the actual solution depending on the value to be optimized.
For example, if you want to minimize time, a better neighbor solution is the one that takes
less time to complete the process and a worse solution is the one that completes the
process in a long time.
Figure 3.18 shows the probability of selecting a better and worse solution,
depending on the progress of a run of 1000 iterations. In this figure, it can be seen that a
better solution always has a 100% probability of being selected, while a worse solution
has a variable probability that decreases with respect to the iterations.
Figure 3.18. Probability of neighbor solution (better and worse) of becoming the new actual solution.
From this point on, a new current solution is already in place and the iterative
process starts again. Throughout the mutations, better results will be found, while new
search areas are evaluated. Once the stop condition is met, the algorithm performs a final
analysis and delivers the best solution obtained along the run.
0%
20%
40%
60%
80%
100%
120%
0 200 400 600 800 1000 1200
pro
bab
ility
iterations
probability (worse solution) probability (better solution)
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4. Chapter Four Simulation models 4.1 Introduction
To solve the problem of the synthesis of optimum operating procedures through the
dynamic optimization framework proposed and described in Chapter 3, dynamic
simulation models must be developed and to be integrated with metaheuristic
optimization algorithms.
Modeling is the process of representing a physical phenomenon, or real-world
object using abstract notations including but not limited to mathematical symbols [114].
System modeling according to El Hefni and Bouskela [115] is referred to as deriving from
physical laws a valid set of mathematical equations that describe the system behavior in
order to assess quantitatively how the system performs its duties according to some
prescribed mission. Steady-state or static modeling is useful for computing isolated
operating states of the system, while dynamic modeling has the aims of computing the
system state variables changes over time. Static modeling is mainly used for system
sizing and optimization at the design stage, as opposed to dynamic modeling that is
mainly used for system redesign and optimization at the operation stage. The models
developed in this thesis are dynamics models.
Similarly, El Hefni and Bouskela [115] define simulation as an experiment
conducted on a model, therefore, the simulations are numerical experiments conducted
with a computer-executable version of the model, which is usually obtained by compiling
the model expressed in a computer language into machine-executable code. The
computer language used for modeling is called a modeling language. A simulation run of
a dynamic model consists essentially of solving an initial value problem, i.e., a set of
differential-algebraic equations with given initial values for the state variables and given
values for the inputs. Inputs with fixed values all along a simulation run are often called
parameters. Experiments with the same model differ depending on the numerical values
provided as inputs of the model and to the initial values of the state variables. Those
values must be physically consistent in order to provide correct results. From a numerical
70
point of view, any input can produce numerical results, but not any input can produce
valid numerical results.
4.2 Drum boiler modeling 4.2.1 Introduction
In order to evaluate an approach for managing the thermal power plant flexible operation
based on the steam generation process optimization, a case study is discussed in
Chapter 6 focuses on the minimization of the drum boiler startup time. Therefore, a drum
boiler dynamic simulation model must be developed and validated.
In thermal power plants, steam generation is carried out through a steam generator
or a boiler. The steam generator is a device that produces high pressure and high-
temperature steam for energy generation. This process is carried out by transferring heat
from flue gases from a furnace or a gas turbine exhaust to water contained in the riser
and downcomer waterwalls in order to produce steam through a boiling process (see
Figure 4.1). Then, in a pressure vessel known as a drum boiler, the saturated steam is
separated from liquid water. The steam is dried inside the drum boiler and sent to the
superheater to be heated above the saturation temperature, then it is piped through the
main steam lines to the steam turbine in order to produce electrical power. Due to its
important function in the steam generation process, the drum boiler is considered the
most critical element in the steam generator: it is in this equipment in fact where the steam
quality and steam flow rate that influence the generation of energy in the steam turbine
are regulated. The steam generator typically is composed of the drum boiler, mud drum,
a water circulation loop, feedwater system, and recirculation pumps, as well as a thermal
energy supply system. The water circulation loop is composed of the downcomer and
riser waterwalls.
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Figure 4.1. A drum boiler basic configuration.
A typical drum boiler configuration consists of a water circulation loop and a heat
energy system [116]. The water circulation loop is composed of a steam drum, mud drum,
the downcomer waterwalls tubes, and the riser waterwalls tubes. The steam drum is the
top drum of a boiler where all of the generated steam is collected before entering the
distribution system. The steam drum has the function of controlling the steam generator
water level since the loss of water level can damage boiler equipment: excessively high-
water levels can result in wet steam, which can cause operational upsets. The mud drum
is the lower drum in a boiler. The mud drum is filled with water and functions as a settling
point for solids in the boiler feedwater. Sediment accumulated in the bottom of the mud
drum is removed by water blowdown. Downcomer waterwalls are a set of pipes leading
from the top to the bottom of the drum boiler, and through them, the water is transferred
from the steam drum to the mud drum. The downcomer is the cooler water line that goes
from the upper drum to the lower drum. Riser waterwall tubes contain boiler feedwater
that is heated by radiant heat from flue gases and boiled to produce steam that flows
upward to the steam drum. The riser is the hotter water line that goes from the mud drum
to the steam drum. The heat energy system supplies heat from the flue gases to the water
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flowing down the riser waterwall tubes in order to regulate the boiling process. Gravity
induces the saturated steam to rise, leading to circulation in the riser-drum-downcomer
loop. The feedwater is supplied to the steam drum through a centrifugal pump, and
saturated steam is taken from the drum through a control valve to the superheaters and
then to the turbine. A 3D model of a typical drum boiler configuration is shown in Figure
4.2.
Figure 4.2. A drum boiler’s basic configuration.
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4.2.2 Drum boiler mathematical modeling
The simulation model developed in this thesis is based on the Astrom and Bell model
[105]. The model assumes a global mass balance and water co-existence in two phases:
liquid and steam inside the drum, as well as a water thermodynamic state at the phase
boundary. Feedwater from the condenser enters the steam drum, and saturated steam is
extracted. For simplicity, the complex configurations and geometries of the drum boiler
are neglected as the model considers bulk flows, volumes, and masses. Alos spatial
variations in the process variables such as in individual geometric features, and fin and
pipes arrangements in the risers and downcomers are not considered. Moreover, this
model assumes an adiabatic behavior with zero heat losses between the water inside the
drum and the drum and pipes’ metal walls. Therefore, it assumes that the water and metal
temperatures are in thermodynamic equilibrium within the drum. Despite these
simplifications, the resulting lumped parameter model is capable of capturing the overall
behavior of the drum boiler. The behavior of the boiler furnace in a coal-fired power plant
or exhaust gases of a gas turbine was modeled through a heat supply system that heated
and evaporated the water in the rising tubes.
The global mass balance in the drum boiler is shown in Equation (4.1):
𝑑
𝑑𝑡[𝜌𝑠𝑉𝑠𝑡 + 𝜌𝑤𝑉𝑤𝑡] = 𝑞𝑓 − 𝑞𝑠 (4.1)
where 𝜌𝑠 is the specific steam density, 𝑉𝑆𝑇 is the total system steam volume, 𝜌𝑤 is the
specific water density, 𝑉𝑤𝑡 is the total system water volume, 𝑞𝑓 is the feedwater mass flow
rate, and 𝑞𝑠 is the steam mass flow rate.
The global energy balance in the drum boiler can be written as:
𝑑
𝑑𝑡[𝜌𝑠ℎ𝑠𝑉𝑠𝑡 + 𝜌𝑤ℎ𝑤𝑉𝑤𝑡 − 𝜌𝑉𝑡 +𝑚𝑡𝐶𝑝𝑡𝑚] = 𝑄 + 𝑞𝑓ℎ𝑓 − 𝑞𝑠ℎ𝑠 (4.2)
where ℎ𝑠 is the specific steam enthalpy, ℎ𝑤 is the specific water enthalpy, 𝜌 is the
mixture density, 𝑉𝑡 is the total system volume, 𝑚𝑡 is the total mass of the metal tubes and
the drum, 𝐶𝑝 is the specific heat of the metal, 𝑄 is the heat supplied to the tube, and ℎ𝑓 is
the feedwater enthalpy per unit of mass.
74
The total volume of the drum, downcomer, and riser (𝑉𝑡) is determined by the total
steam and water volumes as shown below:
𝑉𝑡 = 𝑉𝑠𝑡 + 𝑉𝑤𝑡 (4.3)
The global mass and energy balance for the riser section is represented by
Equations (4.4) and (4.5), respectively:
𝑑
𝑑𝑡[𝜌𝑠𝛼𝑣𝑉𝑟 + 𝜌𝑤(1 − 𝛼𝑣)𝑉𝑟] = 𝑞𝑑𝑐 − 𝑞𝑟 (4.4)
𝑑
𝑑𝑡[𝜌𝑠ℎ𝑠𝛼𝑣𝑉𝑟 + 𝜌𝑤ℎ𝑤(1 − 𝛼𝑣)𝑉𝑟 − 𝜌𝑉𝑟 +𝑚𝑟𝐶𝑝𝑡𝑠] = 𝑄 + 𝑞𝑑𝑐ℎ𝑤 − 𝑞𝑠(𝛼𝑟ℎ𝑐 + ℎ𝑤) (4.5)
where 𝛼𝑣 is the average volume fraction, 𝑉𝑟 is the riser volume, 𝑚𝑟 is the riser
mass, 𝑡𝑠 is the steam temperature, 𝑞𝑑𝑐 is the downcomer flow rate, 𝛼𝑟 is the steam quality
at the riser outlet, and ℎ𝑐 = ℎ𝑠 + ℎ𝑤 is the condensation enthalpy.
The momentum balance for the downcomer-riser loop is:
(𝐿𝑟 − 𝐿𝑑𝑐)𝑑𝑞𝑑𝑐𝑑𝑡
= (𝜌𝑤 − 𝜌𝑠)𝛼𝑣𝑉𝑟𝑔 −𝑘(𝑞𝑑𝑐)
2
2𝜌𝑤𝐴𝑑𝑐 (4.6)
where 𝐿𝑟 is the riser lengths, 𝐿𝑑𝑐 is the downcomer lengths, 𝐴𝑑𝑐 is the downcomer
area, and 𝑘 is a dimensionless friction coefficient.
The mass balance for the steam under the liquid level in the steam drum is:
𝑑
𝑑𝑡(𝜌𝑠𝑉𝑠𝑑) = 𝛼𝑟𝑞𝑟 − 𝑞𝑠𝑑 − 𝑞𝑐𝑑 (4.7)
where 𝑉𝑠𝑑 is the volume of steam under the liquid level in the drum, 𝑞𝑠𝑑 is the steam
flow rate through the liquid surface in the drum, 𝑞𝑟 is the flow rate out of the risers, and
𝑞𝑐𝑑 is condensation flow.
The behavior of condensation flow in the drum and the steam flow rate through the
liquid surface in the drum are given by Equations (4.8) and (4.9):
𝑞𝑑𝑐 =ℎ𝑤 − ℎ𝑓ℎ𝑐
𝑞𝑓 +1
ℎ𝑐(𝜌𝑠𝑉𝑠𝑑
𝑑ℎ𝑠𝑑𝑡+ 𝜌𝑤𝑉𝑤𝑑
𝑑ℎ𝑤𝑑𝑡
+ (𝑉𝑠𝑑 − 𝑉𝑤𝑑)𝑑𝑝
𝑑𝑡+𝑚𝑑𝐶𝑝
𝑑𝑡𝑠𝑑𝑡) (4.8)
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𝑞𝑠𝑑 =
𝜌𝑠𝑇𝑑(𝑉𝑠𝑑 − (𝑉𝑠𝑑)
0) + 𝛼𝑟𝑞𝑑𝑐 + 𝛼𝑟𝛽(𝑞𝑑𝑐 − 𝑞𝑟) (4.9)
where 𝑉𝑤𝑑 is the volume of water under the liquid level in the drum, 𝑚𝑑 is the mass
in the drum, (𝑉𝑠𝑑)0 denotes the volume of steam in the drum in the hypothetical situation
when there is no condensation of steam in the drum, and 𝑇𝑑 is the residence time of the steam in the drum, which is approximated by:
𝑇𝑑 =
𝜌𝑠(𝑉𝑠𝑑)0
𝑞𝑠 (4.10)
From the distribution of the steam below the drum level, the drum level can be
modeled using the equation of water in the drum:
𝑉𝑤𝑑 = 𝑉𝑤𝑡 − 𝑉𝑑𝑐 − (1 − 𝛼𝑣)𝑉𝑟 (4.11)
Since the drum has a complex geometry configuration, the liquid level changes
can be described by the wet surface 𝐴𝑑 at the operating level. The deviation of the drum
level measured from its normal operating level is:
𝑙 =𝑉𝑤𝑑 + 𝑉𝑠𝑑𝐴𝑑
= 𝑙𝑤 − 𝑙𝑠 (4.12)
The term 𝑙𝑤 represents level variations caused by changes in the amount of water
in the drum, and the term 𝑙𝑠 represents variations caused by the steam in the drum.
In summary, the state variables that describe the behavior of the system are: drum
pressure 𝑝, total water volume 𝑉𝑤𝑡, steam quality at the riser outlet 𝛼𝑟, and volume of
steam under the liquid level in the drum 𝑉𝑠𝑑 . The parameters required by the model are:
drum volume 𝑉𝑑, riser volume 𝑉𝑟 , downcomer volume 𝑉𝑑𝑐 , drum area 𝐴𝑑 at the normal
operating level, total metal mass 𝑚𝑡, total riser mass 𝑚𝑟, friction coefficient in downcomer-
riser loop 𝑘, residence time 𝑇𝑑 of steam in the drum, and parameter 𝛽 in the empirical
equation steam flow rate through the liquid surface in the drum 𝑞𝑠𝑑.
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4.2.3 Thermal stress modeling
The thermal stresses were determined according to the general equations for radial,
tangential, and axial thermal stresses in a thick-walled pressure vessel under a radial
thermal gradient shown in the work of Mirandola et al. [59]:
𝜎𝑟 =𝛼𝐸
(1 − 𝜇)𝑟2(𝑟2 − 𝑎2
𝑏2 − 𝑎2∫ 𝑇𝑟𝑑𝑟𝑏
𝑎
−∫ 𝑇𝑟𝑑𝑟𝑟
𝑎
) (4.13)
𝜎𝑡 =𝛼𝐸
(1 − 𝜇)𝑟2(𝑟2 + 𝑎2
𝑏2 − 𝑎2∫ 𝑇𝑟𝑑𝑟𝑏
𝑎
−∫ 𝑇𝑟𝑑𝑟𝑟
𝑎
− 𝑇𝑟2) (4.14)
𝜎𝑎 =𝛼𝐸
(1 − 𝜇)(
2
𝑏2 − 𝑎2∫ 𝑇𝑟𝑑𝑟𝑏
𝑎
− 𝑇) (4.15)
𝜎𝑉𝑀 = √𝜎12 + 𝜎22 + 𝜎32 − 𝜎1𝜎2 − 𝜎1𝜎3 − 𝜎2𝜎3 (4.16)
where 𝜎𝑟, 𝜎𝑡, and 𝜎𝑎 are the radial, tangential, and axial stresses, respectively. 𝛼
is the thermal expansion, 𝐸 is Young’s modulus, 𝜇 is Poisson’s ratio, 𝑟 is a variable radius,
𝑎 is the inside radius, 𝑏 is the outside radius, 𝜎𝑉𝑀 is the von Mises stress, and 𝜎1, 𝜎2, and
𝜎3 are the main stresses. 𝑇 represents the metal temperature, which is considered
equivalent to the water saturation temperature inside the drum.
4.2.4 Drum boiler simulation model validation
The drum boiler simulation model was implemented and tested on the OpenModelica
modeling and simulation environment. OpenModelica is a free and open-source
environment based on the Modelica language for modeling, simulating, optimizing, and
analyzing complex dynamic systems [117]. The OpenModelica development is managed
by a board which includes researchers from the industrial and academic sector such as
ABB AG, University of Hamburg, Bosch Rexroth and FH Bielefeld in Germany, Politecnico
di Milano in Italy, Linköping University in Sweden, RTE-France and EDF in France and
77
VTT Technical Research Centre of Finland. Figure 4.3 shows the drum boiler model
developed in the OpenModelica OMEdit graphic environment.
Figure 4.3. Drum boiler simulator in OpenModelica.
The drum boiler model was validated by executing the reference startup sequence
published by Belkhir et al. [98] and comparing the pressure, temperature, thermal stress,
heat supplied, steam flow, and steam flow regulation profiles. Figures 4.4 to 4.9 show the
reference results reported by Belkhir et al. [98] and those obtained with the model being
validated. From the comparison of these profiles, it can be concluded that the model is
satisfactorily validated and in excellent agreement.
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Figure 4.4. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of heat supplied.
Figure 4.5. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of the steam regulator valve position.
79
Figure 4.6. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of the output steam from the drum boiler.
Figure 4.7. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of the pressure in the drum boiler.
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Figure 4.8. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of the steam temperature in the drum boiler.
Figure 4.9. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of the thick-walled von Mises stresses.
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4.3 Modeling of Combined Cycle Power Plants (CCPP) and Combined Heat and Power Systems (CHP)
4.3.1 Introduction
An approach for the synthesis of optimum operating procedures of the entire thermal
power plant, as well as for a combined heat and power system are proposed. This
approach focuses on finding the optimal control valves sequences that minimize the
power plant operational times and the efficient supply of thermal energy for the selected
industrial process using the dynamic optimization framework described in Chapter 3,
which is based on metaheuristic optimization algorithms coupled with a dynamic
simulation model. In this context, the dynamic simulation models of the power plant and
CHP system must be developed and validated. A case study for the synthesis of optimum
operating procedures for a power plant and the efficient supply of thermal energy of a
cogeneration system will be addressed in Chapter 6.
According to data from the National Electric System in Mexico (SEN) [14] the
dominant generation technology in the SEN is the combined cycle power plant since it
represents 36.5% of the total installed capacity and 51% of total gross generation.
Likewise, the SEN projections suggest that this trend will be maintained by 2033 and that
combined cycle power plants will provide similar amounts of energy to the system. Also
considering the flexible generation studies of conventional thermal power plants
presented by [25, 28 and 91] and the comparison of the thermal power plant's operational
flexibility capabilities based on evaluation of the three main technological parameters of
flexible operation (turndown, ramp rate and operating times) shown in table 1.1 of Chapter
1, it was concluded that the best alternative to develop flexible operation capabilities are
the combined cycle plants; thus, the power plant dynamic simulation model development
must be focused on this kind of power plant.
Combined Cycle Power Plants (CCPP's) are the most efficient power plants
operating on the power grids throughout the world [114]. Unlike other electricity
production options such as Gas Turbine and Steam Turbine alone, CCPP´s can offer up
to 62% efficiency [115]. A CCPP integrates two thermodynamic cycles, operating at a
high- and low-temperature range, respectively, to yield higher plant efficiency and output
than either cycle operating alone [116]. According to the International Energy Agency
82
(IEA), the CCPP´s plays a key role in the transition to liberalized energy markets, since
they represent an efficient coupling between the fossil-fuel-based electric power
generation with the growing variable renewable energy generation.
Additionally, as reported by the International Renewable Energy Agency (IRENA)
[18], the coupling of high-efficiency thermal power plants such as CCPP's with process
steam plants that provide thermal energy for high-demand industrial processes can
increase the thermodynamic efficiency and decrease of greenhouse gas emissions of the
systems. Thermodynamically, cogeneration based on combined cycle power plants
provides the most efficient use of fuel: heat remaining in the exhaust gases from the gas
turbine is captured by the heat recovery steam generator to generate electricity and by
the process, steam plant to produce thermal energy for domestic or industrial purposes
[118].
4.3.2 CCPP operation
Combined cycle plants are formed by a topping cycle (gas turbine-based) and a bottoming
cycle (steam turbine-based). Each cycle operates with separate working fluids and the
two cycles are integrated by the exchange of heat from the high-temperature (topping
cycle) to the lower temperature (bottoming cycle). Between the gas turbine and the steam
turbine is a waste heat recovery steam generator (HRSG), which takes the heat from the
exhaust of the gas turbine and generates high-pressure (HP) steam for the steam turbine.
Heat input must occur in the topping cycle but may additionally occur in the bottoming
cycle with supplementary firing or through renewable or process heat integration [114,
116]. The operation of the gas turbine is described by the Brayton cycle (topping cycle),
while the Rankine cycle (bottoming cycle) describes the thermodynamics of the water-
steam cycle of the power plant. The main challenge in these systems is to obtain an
integration level that maximizes the efficiency at an economic cost at all times. In these
systems, the recovers energy by water-steam cycle can be used for different purposes
such as the power generation or simultaneous production of thermal energy and
electricity (Combined Heat and Power Systems).
Another advantage of the CCPP´s related to system efficiency is the performance
improvement in terms of reduction of pollutant emissions. The combined cycle power
83
plant uses less fuel per kWh and so it is much cleaner than coal-fired power plants; thus,
CCPP's emit by up to 90% less nitrogen oxide (NOx) and virtually no sulfur dioxide (SO2)
and they can reduce the CO2 emissions by up to 75% [117].
Combined cycle power plants are flexible in different ways. Regarding the fuel,
they can operate burning a wide variety of fuels, such as natural gas, coal, oil fuels, diesel,
etc. CCPPs require less space than an equivalent coal or nuclear power plant and less
constraints on site due to lower environmental impact. CCPPs can be installed close to
the demand points, thus reducing the need for long transmission lines and decreasing the
overall cost of electricity for final consumers. Since their operating dynamic response
characteristics are superior to other power plants, such as fuel-oil and nuclear power
plants, CCPPs are much more able to adapt to fluctuations in the electricity demand by
improving their operating capabilities.
The basic configuration of a combined cycle power plant is illustrated in Figure
4.10; the main components are:
Gas turbine (GT);
Heat Recovery Steam Generator (HRSG);
Steam Turbine (ST);
Steam Line (SL);
Condenser (CD);
Electric Generator or Alternator (EG).
84
Figure 4.10.A combined cycle power plant basic configuration.
85
The gas turbine (GT) systems are governed by the thermodynamic Brayton cycle,
which is one of the most efficient for converting the chemical energy of gas fuels to
mechanical power. Since GT provides a large part of the electrical power (about 60%) in
the combined cycle and supplies the thermal energy required by the steam cycle is
considered as the most important equipment of the power plant. The GT is constituted by
three main elements, a compressor which is coupled to a turbine and a combustion
chamber in between them, as shown schematically in Figure 4.11.
Figure 4.11. Gas turbine structure.
For the GT operation, air at atmospheric conditions enters the compressor and
experiment an adiabatic compression until the required pressure for combustion. Thus,
an increase in air temperature and pressure is carried out. In the combustion chamber,
the fuel is mixed with compressed air, then they are burned under constant pressure
conditions to convert the fuel’s chemical energy into thermal energy. From the combustion
process gases at high temperature and high-pressure are generated and subsequently
expanded in the turbine, generating enough mechanical power to drive the compressor
and the electrical generator.
The heat recovery steam generator (HRSG) provides the thermodynamic link
between the gas turbine and steam turbine in a combined cycle power plant. HRSG is a
high-efficiency steam boiler in which the heat exchangers use the hot gases from the gas
turbine to produce steam and to increase the steam temperature beyond the saturation
point so that it can be expanded in the steam turbine [119]. HRSG can use one or more
86
water/steam cycles at different pressure levels. The basic HSRG system is integrated by
the following units: an economizer, an evaporator associated with a drum boiler, and a
superheater [120], as shown schematically in Figure 4.12.
Figure 4.12. The basic configuration of a HRSG with one pressure level.
The economizer (ECO) is a heat exchanger used to preheat the feedwater entering
the drum in order to replace the steam produced and delivered to the superheater. This
component usually is located in the colder zone of the GT exhaust gas, downstream of
the evaporator.
The evaporator (EV) has the function of transforming the heated liquid (water) from
the drum to saturated steam. In this heat exchanger, the fluid enters as a liquid and exits
as saturated steam. The evaporator system is connected to the drum via downcomer
pipes, riser pipes, and distribution manifolds.
The superheater (SH) is designed to transform and transfer the saturated steam
from the steam drum to superheated steam for injection in the steam turbine. This drying
process of the steam is typically performed at constant pressure. The SH is normally
located in the hotter gas stream close to the inlet of the exhaust gases from the gas
turbine.
The steam drum boiler is the connection point among economizer, evaporator, and
superheater. The drum is designed to act as a storage tank as well as a separator for the
saturated steam and liquid phase of the water mixture. In the drum boiler, the preheated
87
feedwater from the economizer is the input and the saturated steam from the evaporator
is the output.
The steam line (SL) is the piping system that makes the connections between the
HRSG, the steam turbine, and the condenser. The steam from the HRSG flow through
pipes and delivered to the ST or the condenser using the bypasses when the steam
turbine is in the offline state [121]. The SL is equipped with admission valves, vent valves,
and bypass systems, depending on the manufacturer, these can have different
dimensions or configurations. A schematic representation of the SL is shown in Figure
4.13.
Figure 4.13. Steam line schematic representation.
The steam turbine (ST) is a mechanical device that extracts thermal energy from
pressurized steam and transforms it into mechanical work [122]. The ST operates on the
Rankine cycle using high pressure and temperature steam (high-enthalpy) provided by
HRSG. The ST is driven by the pressure of steam discharged at high velocity against the
turbine vanes. After that, the mechanical work produced by the ST is converted to
electrical energy through an electric generator.
The steam turbine consists of a set of stationary and rotating blades. The stationary
blades are connected to the casing and a set of rotating blades which are connected to
the shaft. The high-enthalpy energy stored on the steam is converted to kinetic energy
in the stationary blades and directs the steam flow onto the rotating blades. The rotating
88
blades transform the kinetic energy in impulse and reaction forces caused by pressure
drop, which results in the rotation of the turbine rotor [123].
In order to optimize the water-steam cycle in the steam turbine, different pressure
levels are chosen. The Rankine cycle efficiency can be improved by increasing the steam
enthalpy that enters the turbine.
Usually, a steam turbine of a power plant consists of three stages which are a
function of the operating pressure ranges, High Pressure (HP), Intermediate Pressure
(IP), and Low Pressure (LP) turbine, as are shown in Figure 4.14.
Figure 4.14. Schematic diagram of a steam turbine.
The condenser in a power plant is a heat exchanger used to condense exhaust
steam from a steam turbine into the water at a very low pressure that can be reused in
the boiler to again convert it to steam [124]. Like the economizer, evaporator, and
superheater, the steam condenser of a power plant boiler is a critical heat exchanger in
the process. Poor condenser performance in heat transfer causes a decrease in the
power plant thermodynamic efficiency, while impurities introduced to the condensate can
cause severe steam generator damage.
The steam condensation process is carried out by passing the wet steam around
several cold-water tubes in the heat exchanger. The liquid water is collected at the bottom
of the condenser and returned to the HRSG using extraction pumps, to continue the
water-to-steam cycle. The exhaust steam must be condensed since pumping water
89
requires less energy when compared to pumping steam back to the boiler. A schematic
representation of a power plant condenser is shown in Figure 4.15.
Figure 4.15. Schematic diagram of a power plant condenser.
The electric generator or alternator is the device used to convert the rotating
mechanical energy into electrical energy [125]. In thermal power plants, the most common
type of generator used is the synchronous alternator. It consists of a stationary stator with
the output windings arranged around its periphery and a rotating, driven rotor with direct
current windings acting as an electromagnet [126]. When the electromagnet rotates, it
generates a current in the stator. In operation, it generates up to 24,000 V of current. The
power that is generated is alternating current, which is transformed to the voltage, rectified
(converted) to direct current (because direct current can be transported over large
distances efficiently), transmitted over transmission lines as direct current, and then
inverted back to alternating current at the point of application. The turbine and generator
rotors are connected through a coupling and the rotation of the turbine blades causes the
rotation of the generator rotor shaft. The main components of an electric generator are
the engine, alternator, fuel system, voltage regulator, lubrication system, cooling and
exhaust systems, battery charger, and control panel.
90
4.3.3 CHP operation
The combined heat and power systems are an energy-efficient technology that works
according to the principle of generating electrical power and captures the heat that would
otherwise be wasted to provide useful thermal energy, such as steam or hot water that
can be used for space heating, cooling, domestic hot water, and industrial processes
[127]. These systems use around 90% of the heat available from the fuel consumed,
saving significant amounts of primary energy and CO2 emissions [81]. That makes CHP
systems highly efficient and climate-friendly.
Nearly two-thirds of the energy used by thermal power plants in the generation of
electricity is wasted in the form of heat discharged to the atmosphere via power station
cooling towers. By capturing and using heat that would otherwise be wasted, the CHP
systems can achieve efficiencies above 65 percent, compared to 45 percent for typical
thermal power plant technologies [127].
According to [127], the CHP systems based on thermal power plants focus on
increasing energy security and improve the energy efficiency of the electric power system,
as well as to diversify and enhance the applicability of the power plant. Usually, the two
most common CHP system configurations are:
CHP based on hot exhaust gases: Fuel is combusted in a gas turbine or internal combustion engine, which is coupled
to an electric generator that produces electrical power. The thermal energy that normally
will be lost is mostly recovered to provide useful thermal energy, usually in the form of
steam or hot water.
CHP based on low-pressure steam: Based on steam turbines, the fuel is burned in a boiler to produce high-pressure
steam. This steam is sent to a steam turbine that is coupled to an electric generator that
produces electrical power. Then, the low-pressure steam that exits of the turbine is
directly used to produce useful thermal.
The CHP systems are often used in applications with steady thermal and electric
loads. Beyond the typical uses for heating and cooling, CHP systems are well suited for
the industrial sector such as refineries, wastewater treatment plants, chemical plants, and
in general for processes with significant thermal and electric demands.
91
The generic arrangement of the two typical configurations of CHP systems are
shown in Figures 4.16 and 4.17.
Figure 4.16. CHP system based on hot exhaust gases, based on [127].
Figure 4.17. CHP system based on low-pressure steam, based on [127].
92
According to Al-Shemmeri [128], a typical configuration of a CHP system consists
of three basic components: a primary engine in which the fuel is converted into
mechanical and/or thermal energy, an electric generator or alternator to transform
mechanical energy into electricity and a heat recovery system to collect the heat
produced. The operating scheme of a CHP system based on energy recovery from the
hot exhaust gas is shown schematically in Figure 4.18.
Figure 4.18. Operating scheme of a CHP system based on energy recovery from the hot exhaust gas.
The section corresponding to electrical power generated by a gas turbine is shown
in gray color. The exhaust gases can be used to produce electrical power and thermal
energy independently. Additional electric power can be generated from the hot exhaust
gas through a HRSG system, a steam turbine, and an electric generator, which is known
as a combined cycle power plant (presented in blue color). Otherwise, thermal energy
can be produced through a heat exchanger system using the hot exhaust gas available
energy (showed in orange color).
The baseline configuration of a gas turbine exhaust gas derivation CHP system in
a combined cycle power plant is shown schematically in Figure 4.19. Module I represent
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the original configuration of the combined cycle power plant consisting of a gas turbine,
a heat recovery steam generator, and a steam turbine. In this module, electricity is
generated from fuel thermal energy by two thermodynamics cycles. The first one
corresponds to a Brayton Cycle, where the combustion of natural gas produces work on
the shaft in the gas turbine. Furthermore, high-temperature exhaust gases from the gas
turbine are used by a heat recovery steam generator to produce high pressure and
temperature steam (Rankine Cycle), generating electricity using a steam turbine. Part of
the high-temperature exhaust gases at the gas turbine outlet are derived as the heat
source to produce the required thermal energy for the needs of the industrial processes.
Individual simulation models of combined cycle power plant and CHP system are
described in the next sections.
94
Figure 4.19. The basic configuration of combined heat and power systems based on high-temperature exhaust gases.
95
4.3.4 CCPP mathematical modeling
The operational behavior of the power plant is achieved by determining its thermodynamic
properties. Usually, these properties are found by using physical modeling based on
mass, energy, and heat balance equations. Definitions of these properties are widely
provided in several previous studies [88, 129, 130, and 131]. Governing equations for the
combined cycle power plant components are presented as follows:
Air Compressor (AC):
The compressor work rate is a function of air specific heat 𝐶𝑝𝑎, air mass flow rate
�̇�𝑎, the temperature a difference between the compressor inlet and outlet 𝑇𝑂𝐶−𝑇𝐼𝐶,
compressor pressure ratio 𝑃𝑂𝐶𝑃𝐼𝐶
, compressor isentropic efficiency 𝜂𝐶 and can be expressed
as follow:
�̇�𝐶 = �̇�𝑎 ∙ 𝐶𝑝𝑎 ∙
(
(
𝑇𝐼𝐶+(
((𝑃𝑂𝐶𝑃𝐼𝐶
)
𝛾𝑎−1𝛾𝑎)−𝑇𝐼𝐶
)
𝜂𝐶
)
− 𝑇𝐼𝐶
)
(4.17)
where 𝛾𝑎 is the air specific heat ratio and 𝐶𝑝𝑎 represents a function of temperature
according to Equation 4.18 [132]:
𝐶𝑝𝑎(𝑇) = 1.048 + (3.83𝑇
104) + (
9.45𝑇2
107) − (
5.49𝑇3
1010) + (
7.92𝑇4
1014) (4.18)
Combustion Chamber (CCH):
From the energy balance of the combustion chamber, the fuel flow required by the
cycle is calculated according to the following relationship:
𝑓 = 𝐶𝑝𝑔 ∙ 𝑇𝑂𝐶
𝐿𝐻𝑉 ∙ 𝜂𝐶𝐶+𝐶𝑝𝑓 ∙ 𝑇𝑓+𝐶𝑝𝑐𝑔 ∙ 𝑇𝑂𝐶𝐶
+�̇�𝑠𝑡𝑒𝑎𝑚�̇�𝑎𝑖𝑟
∙𝐶𝑝𝑠𝑡𝑒𝑎𝑚 ∙ 𝑇𝑠𝑡𝑒𝑎𝑚
𝐿𝐻𝑉 ∙ 𝜂𝐶𝐶+𝐶𝑝𝑓𝑇𝑓+𝐶𝑝𝑐𝑔𝑇𝑂𝐶𝐶
(4.19)
where 𝐶𝑝𝑔 is the combustion gases specific heat, 𝑇𝑜𝑐𝑐 is the temperature of flue
gases at the outlet of the combustion chamber, 𝐿𝐻𝑉 is the lower heating value of the
96
fuel, 𝜂𝑐𝑐 is the efficiency of the combustion chamber, 𝐶𝑝𝑓𝑢𝑒𝑙 is the specific heat capacity
of the fuel, 𝑇𝑓 is the temperature of the fuel at the inlet of the combustion chamber, �̇�𝑠𝑡𝑒𝑎𝑚
is the mass steam flow at the combustion chamber inlet, 𝐶𝑝𝑠𝑡𝑒𝑎𝑚 is the specific heat
capacity of the steam and 𝑇𝑠𝑡𝑒𝑎𝑚 is the temperature of the steam at the inlet of the
combustion chamber.
Gas Turbine (GT): The gas turbine output power can be expressed as a function of its input and output
temperatures, isentropic efficiency, and pressure ratio as follows:
𝑊𝐺𝑇 = �̇�𝑔 ∙ 𝐶𝑝𝑔∙
(
𝑇𝑂𝐶𝐶 − 𝑇𝑂𝐶𝐶 (1− 𝜂𝐺𝑇 (1 − (
𝑃𝑂𝐶𝐶𝑃𝑂𝐺𝑇
)
1−𝛾𝑔𝛾𝑔))
)
(4.20)
where �̇�𝑔 is the gas turbine flow rate which is the summation of air mass flow rate
and fuel, 𝑇𝑂𝐶𝐶 is the temperature of combustion gases exiting the combustion chamber,
𝜂𝐺𝑇 is the gas turbine isentropic efficiency, 𝑃𝑂𝐶𝐶 is the pressure of combustion gases
exiting the combustion chamber, 𝑃𝑂𝐺𝑇 is the pressure of the outlet hot gases exiting the
gas turbine, 𝛾𝑔 is combustion gases specific heat ratio and combustion gases specific
heat 𝐶𝑝𝑔 to be a function of temperature according to [132] and expressed by Equation
4.21.
𝐶𝑝𝑔(𝑇) = 0.991 + (6.997𝑇
105) + (
2.712𝑇2
107) − (
1.2244𝑇3
1010) (4.21)
Heat Recovery Steam Generator (HRSG): The energy balances for the water/steam cycle and combustion gases, allow to
determine the gas temperature and water properties according to the expressions below:
�̇�𝑔𝐶𝑝𝑔(𝑇𝐼𝐺𝑆𝐻 − 𝑇𝑂𝐺𝑆𝐻) = �̇�𝑆,𝑆𝐻(ℎ𝑂𝑆𝑆𝐻−ℎ𝐼𝑆𝑆𝐻) (4.22)
�̇�𝑔𝐶𝑝𝑔(𝑇𝐼𝐺𝐸𝑉 − 𝑇𝑂𝐺𝐸𝑉) = �̇�𝑆,𝐸𝑉(ℎ𝑂𝑆𝐸𝑉−ℎ𝐼𝑆𝐸𝑉) (4.23)
97
�̇�𝑔𝐶𝑝𝑔(𝑇𝐼𝐺𝐸𝐶 − 𝑇𝑂𝐺𝐸𝐶) = �̇�𝑆,𝐸𝐶(ℎ𝑂𝑆𝐸𝐶−ℎ𝐼𝑆𝐸𝐶) (4.24)
where �̇�𝑆,𝑆𝐻, �̇�𝑆,𝐸𝑉 and �̇�𝑆,𝐸𝐶 are the steam mass flow rate in the superheater,
evaporator, and economizer, respectively. Meanwhile, 𝑇𝐼𝐺𝑆𝐻, 𝑇𝐼𝐺𝐸𝑉 and 𝑇𝐼𝐺𝐸𝐶 are the
respective temperatures of combustion gases entering the superheater, evaporator, and
economizer. In addition, 𝑇𝑂𝐺𝑆𝐻, 𝑇𝑂𝐺𝐸𝑉 and 𝑇𝑂𝐺𝐸𝐶 are the temperatures of the combustion
gases exiting to superheater, evaporator, and economizer. On the other hand, (ℎ𝑂𝑆𝑆𝐻 ,
ℎ𝑂𝑆𝐸𝑉 ), (ℎ𝑂𝑆𝐸𝐶 , ℎ𝐼𝑆𝑆𝐻) and (ℎ𝐼𝑆𝐸𝑉 , ℎ𝐼𝑆𝐸𝐶) are the steam enthalpies at the inlet and outlet in
the superheater, evaporator, and economizer, respectively.
Steam Turbine (ST) and Condenser (CD): For the case of the steam turbine, the output power is expressed in terms of water
mass flow rate �̇�𝑤, superheated steam enthalpy entering the steam turbine ℎ𝐼𝑆𝑇 and
outlet steam enthalpy from the steam turbine ℎ𝑂𝑆𝑇 according to:
𝑊𝑆𝑇 = �̇�𝑊(ℎ𝐼𝑆𝑇−ℎ𝑂𝑆𝑇) (4.25)
The condenser heat balance is described as:
�̇�𝑓𝑤𝐶𝑝𝑓𝑤(𝑇𝑂𝑈𝑇 − 𝑇𝐼𝑁) = �̇�𝑆𝑇𝐸𝐴𝑀(ℎ𝐼𝐶−ℎ𝑂𝐶) (4.26)
where �̇�𝑓𝑤 is the power plant feedwater flow rate, 𝐶𝑝𝑓𝑤 is the power plant
feedwater specific heat, 𝑇𝐼𝑁 and 𝑇𝑂𝑈𝑇 are the inlet and outlet temperatures of the cold fluid
in the condenser, where ℎ𝐼𝐶 and ℎ𝑂𝐶 are the inlet and outlet enthalpies of the hot fluid in
the condenser.
98
4.3.5 CHP mathematical modeling
The performance of the CHP system is directly related to the operational behavior of each
of its components. Mathematical models based on mass, energy, and heat balance
equations are used to determine the thermodynamic properties of each one of its critical
components. From those models, the operational parameters, sizes, and configurations
of the main system components such as heat exchangers, pipelines, insulation, pumps,
and exhaust gases splitter system can be determined. The governing equations for the
cogeneration plant critical components are described below:
Heat Exchanger (HEX): Considering a parallel flow heat exchanger in which the cold and hot fluids enter in
the same direction and position, the temperature of hot fluid is higher in relation to the
cold fluid, the mass flow rate for both fluids is greater than zero, where specific heat
capacities and mass flow rates are assumed to be constant over the entire length of the
HEX. According to [133], the total thermal power exchanged between the hot and cold
fluid is calculated according to the following expression:
𝑊𝐻𝐸 = 𝑈 ∙ 𝐴 ∙
(
(𝑇𝐻,𝑂 − 𝑇𝐶,𝑂) − (𝑇𝐻,𝐼 − 𝑇𝐶,𝐼)
|𝑙𝑛 (𝑇𝐻,𝑂 − 𝑇𝐶,𝑂)
(𝑇𝐻,𝐼 − 𝑇𝐶,𝐼) |
)
(4.27)
where 𝑇𝐶,𝐼 and 𝑇𝐻,𝐼are the cold and hot fluid inlet temperatures, respectively, 𝑇𝐶,𝑂
and 𝑇𝐻,𝑂 are the cold and hot fluid outlet temperatures, 𝑈 is the overall heat transfer
coefficient for the heat exchanger and 𝐴 is the total surface area used for heat transfer.
In the same way, using the correlations suggested in [133] the mean temperature
difference is evaluated as follows:
∆𝑇𝑚 =(𝑇𝐻,𝐼 − 𝑇𝐶,𝐼) − (𝑇𝐻,𝑂 − 𝑇𝐶,𝑂)
𝑙𝑛 ((𝑇𝐻,𝐼 − 𝑇𝐶,𝐼)
(𝑇𝐻,𝑂 − 𝑇𝐶,𝑂))
(4.28)
99
Pipelines (PP): In the design process for high pressure and high-temperature pipes, the effects of
changes in temperature and heat transfer, as well as pressure losses must be considered.
To quantify frictional pressure losses in a pipeline, the Darcy-Weisbach relation is used
according to [134], correlating the characteristics length of the pipe 𝐿𝑃𝐼𝑃𝐸, diameter 𝐷𝑃𝐼𝑃𝐸,
the velocity of the flow 𝑣𝐹𝐿𝑂𝑊, acceleration due to the gravity 𝑔 and Darcy’s friction factor
𝑓: its value is related to the Reynolds number 𝑅𝑒 and the type of flow inside the pipeline
and expressed as follows:
ℎ𝑓 = 𝑓 ∙𝐿𝑃𝐼𝑃𝐸𝐷𝑃𝐼𝑃𝐸
∙𝑣2
2𝑔 (4.29)
Pipeline temperature losses are determined using heat transfer theories of
conduction (Fourier’s equation), convection (Newton's equation) and radiation (Stefan-
Boltzman’s equation), through the pipeline heat flow per unit length calculation as
suggested in [135]:
𝑞
𝐿=
𝑇𝑖 − 𝑇𝑜
12𝜋𝑟𝑖ℎ𝑖
+ ∑𝑙𝑛 (
𝑟𝑖+1𝑟𝑖)
2𝜋𝑘𝑖+
12𝜋𝑟𝑜ℎ𝑜
𝑛𝑖=1
(4.30)
where 𝑇𝑖 and 𝑇𝑜 are the temperatures on the pipe internal and external surfaces,
respectively, 𝑟𝑖 and 𝑟𝑜 are the internal and external radius of the pipe, 𝑟𝑖+1 is the radius of
the pipe along with the variable thickness, 𝑘𝑖 is the conductive heat transfer coefficient for
each pipe material along with the thickness and ℎ𝑖 and ℎ𝑜 are the convective heat transfer
coefficient inside and outside of the pipe, respectively.
To minimize the heat losses, pipeline insulation must be introduced, and its
thickness must be determined. This process is carried out by matching the total pipeline
heat flow to the corresponding heat flow between the surface to be insulated and the
boundary conditions of the environment [136]:
100
𝑇𝑠,𝑜 − 𝑇𝑜1
2𝜋𝑟𝑜ℎ𝑜
=𝑇𝑖 − 𝑇𝑜
12𝜋𝑟𝑖ℎ𝑖
+∑𝑙𝑛 𝑙𝑛 (
𝑟𝑖+1𝑟𝑖)
2𝜋𝑘𝑖+
12𝜋𝑟𝑜ℎ𝑜
𝑛𝑖=1
(4.31)
The cogeneration system design viability can also be quantified in terms of
greenhouse gas emissions that will not be emitted by replacing the system that supplies
thermal energy to the industrial process.
Exhaust Gas Splitter System (EGBS): In order to control efficiently the flow of exhaust gas from the gas turbine for both
the heat recovery steam generator and the process steam plant, an optimal design of the
exhaust gas splitter system is required. The viability of the EGBS is carried out through
the energy balance of the water/steam cycle and exhaust gases in the cogeneration plant
according to the following equation:
�̇�𝐸𝐺,𝐶𝑆𝐶𝑝𝑒𝑔(𝑇𝐼𝐸𝐺𝐶𝑆 − 𝑇𝑂𝐸𝐺𝐶𝑆) = �̇�𝐸,𝐶𝑆𝐶𝑝𝑒(𝑇𝐼𝐸𝐶𝑆 − 𝑇𝑂𝐸𝐶𝑆) (4.32)
where 𝐶𝑝𝑒𝑔, 𝐶𝑝𝑒, �̇�𝐸𝐺,𝐶𝑆 and �̇�𝐸,𝐶𝑆 are the exhaust gases specific heat, electrolyte
specific heat, exhaust gases mass flow rate, and electrolyte mass flow in the cogeneration
system, respectively. At the same time, 𝑇𝐼𝐸𝐺𝐶𝑆 and 𝑇𝑂𝐸𝐺𝐶𝑆 are the temperatures of exhaust
gases entering and exiting from the cogeneration system. Likewise, 𝑇𝐼𝐸𝐶𝑆 and 𝑇𝑂𝐸𝐶𝑆 are temperatures of electrolyte entering and exiting from the cogeneration system,
respectively.
On the other hand, the greenhouse gas emissions amount is mainly related to the
energy produced by the fuel when it is burned. In agreement with the United States,
Environmental Protection Agency (EPA) [137], the greenhouse gas emission's main
component evaluated in processes related to electricity generation is the carbon dioxide
emissions CO2. According to the International Energy Agency (IEA) [138], the CO2
amount produced in a combustion process is a function of the carbon content of the fuel.
The heat content or energy produced is mainly determined by the carbon (C) and
hydrogen (H) content of the fuel. Natural gas has a higher energy content relative to other
fuels; thus, it has a relatively lower CO2-to-energy content.
101
The emission factor is used to quantify the CO2 emissions produced by the fuel in
the combustion process to generate electricity. Mareddy [139] defines an emissions factor
as a representative value that relates the quantity of a pollutant released to the
atmosphere with an activity associated with the release of that pollutant. Usually, this
factor is expressed as the weight of pollutant divided by a unit weight, volume, distance,
or duration of the activity emitting the pollutant (e.g., kilograms of particulate emitted per
Mega gram of coal burned).
The fuel emission factor can be determined as a function of the calorific value of
the fuel, the carbon amount in the fuel and the complete oxidation stoichiometric factor of
carbon to carbon dioxide [139, 140]. The general equation for emissions estimation is as
follows:
𝐸𝐹 =(∑ 𝑛𝑖
𝑛𝑖 ∗ 𝑋𝑚𝑜𝑙 𝑖)
(∑ 𝑁𝐶𝑉𝑚𝑜𝑙 𝑖𝑛𝑖 ∗ 𝑋𝑚𝑜𝑙 𝑖) ∗ 𝐴
(4.33)
where 𝐸𝐹 is the emission factor, 𝑛 is the number of carbon atoms in the fuel, 𝑋𝑚𝑜𝑙 𝑖
is the molar fraction of component i in the fuel, 𝑁𝐶𝑉𝑚𝑜𝑙 𝑖 is the net calorific value as an
ideal gas of component i in 𝑘𝐽 𝑚𝑜𝑙 𝑖⁄ , which can be obtained from Table 1 of the standard
ASTM-D-3588 according to [140]. 𝐴 is the complete oxidation stoichiometric factor.
From the fuel emission factor and the amount of fuel required by the electricity
generation process, CO2 emissions are determined by the following equation:
𝐸𝐶𝑂2 = 𝐸𝐶 ∗ 𝐸𝐹 ∗ (1 − 𝐸𝑅) (4.34)
where 𝐸𝐶𝑂2 are the fuel carbon dioxide emissions in the period evaluated, 𝐸𝐶 is the
energy consumption in the electricity generation process, 𝐸𝐹 is the emission factor, and
𝐸𝑅 overall emission reduction efficiency in percent.
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4.3.6 CCPP simulation model validation
The simulation models are becoming a powerful tool to represents in a realistic way the
behavior of the systems. Therefore, the simulation models must be focused on both the
accuracy and complexity of the system. In this context, if the simulation model, is too
complex it can be infeasible from the mathematical point of view. Likewise, when simple
simulation models are used, the level of detail of the system may be insufficient for
specific aims although the global behavior of the system is suitably reproduced.
A simulation model must be consistent with the research objective and able to use
previously developed knowledge. In this sense, the use of modeling languages facilitates
the design and development of the simulation models. In addition, the modeling libraries
based on reusable component models that collect expert knowledge support facilitates
the rapid development of models through the adaption of existing components to meet
specific needs.
Simulation models of complex systems such as thermal power plants require
languages able to define system behavior through mathematical formulations. In this
context, the object-oriented modeling language Modelica is used to develop the
simulation model of the power plant. Modelica is an open language designed to support
effective library development and model exchange, which is continuously updated and
maintained by Modelica Association [141]. All these properties make Modelica a powerful
language for modeling and efficient simulation of large and complex systems.
Modelica libraries encompass several kinds of components capable of modeling
mechanical, robotic, electrical, process systems, etc. In the last years, several libraries
focused on the design of power plant simulators have been developed. For example,
Modelica provides a wide range of model components for modeling of thermodynamic
systems of industrial processes and power plants in ThermoSysPro [133] or a library
based on the first principle models for modeling of thermal power plants in ThermoPower
[142], as well as the libraries used for modeling of thermo-hydraulic systems in
ThermoFluid [143] or OpenModelica [144]. In this thesis the library used to develop a
combined cycle model is ThermoSysPro.
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ThermoSysPro is a generic library for the modeling and simulation of power plants
and other kinds of energy systems. ThermoSysPro library is developed by Électricité de
France R&D (EDF) and released under open source license [133].
The foundations of the library are based on first physical principles: mass, energy,
and momentum conservation equations, up to date pressure losses and heat exchange
correlations, and validated fluid properties functions. The correlations account for the non-
linear behavior of the phenomena of interest. They cover all water/steam phases, oil,
molten salt, and all flue gas compositions. The granularity of the modeling may be freely
chosen. Some correlations are given by default since they correspond to the most
frequent use cases, but they can be freely modified by the user if needed. This includes
the choice of pressure drop or heat transfer correlations. Special attention is given to the
handling of two-phase flow, as the two-phase flow is a common phenomenon in power
plants.
The library components are written in such a way that there are no hidden or
unphysical equations, that components are independent of each other and to ensure as
much as possible upward and downward compatibility across tools and library versions.
This is particularly important in order to control the impact of component, library or tool
modifications on the existing models.
This library is aimed at providing the most frequently used model components for
the 0D-1D static and dynamic modeling of thermodynamic systems, mainly for power
plants, but also for other types of energy systems such as industrial processes, energy
conversion systems, buildings, etc. It involves disciplines such as thermal-hydraulics,
combustion, neutronics, and solar radiation.
The library aims for the future is to cover all the phases of the plant lifecycle, from
basic design to plant operation. This includes for instance system sizing, verification and
validation of the instrumentation and control system, system diagnostics and plant
monitoring. To that end, the library will be linked in the future to systems engineering via
the modeling of systems properties, and to the process measurements via data
reconciliation and data assimilation.
The library works coupled with the open-source Modelica-based modeling and
simulation environment OpenModelica.
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The combined cycle power plant simulation model is based on a model presented
in [52], which consists of a gas turbine, a heat recovery steam generator (HRSG) with
three evaporating loops (seven superheaters, three evaporators, and six economizers),
a three-stage steam turbine (low, intermediate, and high pressure), an electric generator,
a condenser, several pumps, valves and pipes and proportional integral (PI) controls
systems to limit the drum levels. In Figure 4.20, the combined cycle power plant model in
the OpenModelica OMEdit graphic environment is shown.
The combined cycle power plant model was validated against the load change
scenario published by [52], in which the power plant goes from an initial state (100% load)
to a final state (50% of load) in about 800 seconds. Similarly, mechanical power profiles
in the gas and steam turbines were also compared, in terms of the level measured at the
three drums. Results evaluation is focused on monitoring the electrical power generation
capacity in the two cycles of the power plant, as well as the level of the HRSG drums
since these can lead to steam production inefficiencies, steam quality issues, and power
plant safety risks. Figures 4.21 to 4.28 show the results reported by [52] and those
obtained with our model implementation. As expected, the numerically obtained results
derived simulation profiles that are consistent and very close to the reported ones in [52],
with negligible numerical differences and excellent trends agreement. Accordingly, it can
be concluded that the combined cycle power plant dynamic simulation model
implemented in OpenModelica has been validated since the results reported by [52] were
originally endorsed with operational data of an existing power plant in Vietnam [133]. As
expected, as time progresses the gas turbine mechanical power decreases linearly
almost to an asymptotic value corresponding to the minimum load for the change load
case study, as shown in Figure 4.21. Regarding the steam turbines, the expected non-
linear behavior of mechanical power is shown in Figures 4.22, 4.23 and 4.24. This
mechanical power response is mainly attributed to the dynamic energy exchange
between exhaust gases and water steam in the sixteen-heat exchanger of the steam
generator as is shown in Figure 4.25. Figures 4.26, 4.27 and 4.28 show the dynamic
effect of swelling in the high, intermediate and low-pressure drums, in which the water
level inside the drum increases when the corresponding drum pressure decreases.
105
Figure 4.20. Combined cycle power plant simulator in OpenModelica graphical environment.
106
Figure 4.21. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of gas turbine mechanical power.
Figure 4.22. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of low-pressure steam turbine mechanical power.
107
Figure 4.23. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of intermediate pressure steam turbine mechanical power.
Figure 4.24. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of high-pressure steam turbine mechanical power.
108
Figure 4.25. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of gas turbine exhaust gas temperature.
Figure 4.26. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of high-pressure drum boiler level.
109
Figure 4.27. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of intermediate pressure drum boiler level.
Figure 4.28. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of low-pressure drum boiler level.
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4.3.7 CHP system simulation model validation
The design of the Combined Heat and Power (CHP) system is based on an existing
combined cycle power plant that supplies thermal energy to a high-demand industrial
process. In this context, the simulation model of the CHP system is based on the validated
simulation model of the combined cycle plant discussed above. The combined cycle
power plant simulation model was adjusted in terms of the gas turbine mechanical power
according to operational data of the San Isidro II power plant operating in Chile. For this
study, the steam power cycle configuration between the reference model and a real power
plant are considered to be equivalent since both have a heat recovery steam generator
with three evaporating loops and sixteen heat exchangers, a three-stage steam turbine
(low, intermediate, and high pressure), a condenser, centrifugal pumps, control valves,
and pipes. The steam turbine mechanical power is regulated according to new gas turbine
operating parameters.
Once the combined cycle power plant simulation models that supplies energy to
the CHP system was validated, the exhaust gas splitter system and the thermal energy
generation system must be designed according to the requirements of the selected
industrial process.
The Exhaust Gas Splitter System (EGBS) consists of a splitter and two flow
regulating valves that are synchronously operated to adjust the exhaust gas flow needed
by each component of the CHP system. Between the gas turbine outlet and steam
generator inlet, a splitter is installed distributing the exhaust gases in three different
directions: to the heat recovery steam generator, to the cogeneration plant and to the flue
gas stack. In addition, two control valves are added to regulate the hot gas flows. A control
system for every valve regulates the optimal amount of flows needed by the steam
generator and cogeneration plant, prioritizing thermal energy generation for the high-
demand industrial process. The exhaust gas splitter system design proposed for the CHP
system in the OpenModelica graphical environment is shown in Figure 4.29.
111
Figure 4.29. Exhaust Gas Splitter System (EGBS) proposed for the CHP system in the OpenModelica graphical environment.
112
Regarding the high-demand industrial process and taking into account that the
copper mining industry requires large amounts of fuel in order to provide heat for its
processes. Based on an analysis of data from the International Copper Study Group
[145], which shows Chile as the largest copper producer in the world and copper
extraction represents the largest contribution to the Chilean economy with around 10% of
gross domestic product [146]. Likewise, the Chilean mining industry is the pioneer in
copper refining processes based on copper leach, solvent extraction and electrowinning
technologies [147]. Through these processes, high-purity copper cathodes can be
obtained without the need for prior smelting stages, using process heat at medium-low
temperatures. Electrowinning is significantly important among copper processing
technologies since it is used to produce high-purity metal on large-scales at a reasonable
cost [148]. The electrowinning process cannot tolerate any operational interruption and
must be operating in a continuous mode [89]. Currently, almost all energy required by
electrowinning processes is provided by diesel boiler technologies which are low
efficiency and highly polluting.
The electrowinning plant that is supplied with process heat corresponds to a
copper mining installation present and operating in Chile [149]. This plant produces
approximately 150,000 tons of fine copper per year. Currently, a diesel boiler coupled to
a counterflow plate heat exchanger is used to produce the heat required by the
electrowinning process. Figure 4.30 shows the operating parameters and the
configuration of the actual heating circuit for the electrowinning plant under study.
Additionally, the characteristics of the copper electrowinning process studied herein are
summarized in Table 4.1.
From an energy balance, it is possible to evaluate if the cogeneration system
capacity to produce thermal energy reaches the amount necessary to bring the electrolyte
solution to the electrowinning process operating conditions as described in Figure 4.30
and Table 4.1.
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Figure 4.30. Heating circuit features of the electrowinning plant based on [149].
Table 4.1. Electrowinning process characterization [149].
Parameter Value
Inlet temperature (°C) 27 Desired temperature (°C) 65 Flow rate in the inlet (m3/h) 1,000 Electrolyte density (kg/m3) 1,225 Electrolyte specific heat (J/kg °C) 3,480
In order to supply efficiently the process heat, according to electrowinning process
operational parameters, the proposed cogeneration system operates as follows:
Hot water close to saturation conditions is generated in the power plant.
The design of the hot water circuit involves a water tank, several pipes and pumps, and a counterflow heat exchanger. The hot gases from the gas
turbine are the hot fluid, while the tank water is the cold fluid.
A pumping system and insulated pipes are used to transport hot water to
the electrowinning plant.
In the electrowinning plant, a counterflow heat exchanger is installed in order to heat the electrolyte solution to the required operating conditions.
Hot water from the power plant is the hot fluid, while the electrowinning cells
electrolyte is the cold fluid.
Coupling both systems close the circuit of the water/steam cycle of the
cogeneration plant.
The proposed design of the CHP simulation model is shown in Figure 4.31.
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Figure 4.31. Combined heat and power simulation model – OpenModelica.
115
A splitter location feasibility study was evaluated according to the exhaust gases
operating parameters shown in Table 4.2 which were obtained from a power plant load
change simulation.
Table 4.2. Exhaust gases operating parameters for a load change simulation.
GT Load [%] Exhaust Gases
Q [kg/s] THRSG[°C] THRSG-HP[°C] THRSG-IP[°C] THRSG-LP[°C]
100 606.207 621.078 333.261 236.416 122.302
90 546.002 627.255 327.845 232.209 121.393
80 484.661 636.514 319.886 224.81 119.196
70 424.456 648.874 312.178 218.317 116.554
60 395.442 675.593 311.998 217.854 114.801
50 302.428 701.097 306.561 214.959 112.389
Four alternative scenarios were selected: HRSG inlet, HRSG-HP output, HRSG-
IP output, and HRSG-LP output at different loads ranging from 100% to 50% of the gas
turbine. The results evaluation is presented in Figures 4.32 and 4.33, where all cases are
compared quantifying the energy consumption and exhaust gas temperature decrease.
An energy balance between the exhaust gases and electrolytes is also performed, where
the electrolyte receives thermal energy from the hot exhaust gases.
116
Figure 4.32. Splitter location feasibility in terms of energy consumption.
Figure 4.33. Splitter location feasibility in terms of flue gas temperatures.
117
According to the results shown in Figures 4.34 and 4.35, the alternative HRSG-LP
output is not feasible for cases where the heat load is less than 60% in the steam cycle.
This is attributed to the thermal energy at this location, which is less than the thermal
energy required by the electrowinning process. In regard to the exhaust gases exiting
temperature, for load cases below 80% of these are close to the ambient temperature
and in some cases below zero. For the HRSG-HP and HRSG-IP output alternatives, it is
required to extract about 30% and 45% of the available energy, respectively, in order to
generate electricity in the intermediate and low-pressure turbines given that these are the
ones that produce the most energy within the steam cycle. This energy loss would
represent an average decrease in the generation capacity of the steam cycle close to
30%. Concerning the exhaust gas temperatures for loads from 70% and lower, the system
could not supply steam at temperatures required by intermediate and low-pressure
turbines. For the splitter system located at the HRSG inlet, there is a 15% average
decrease in the exhaust gas temperature for all loads and the operating temperatures are
in the order of 630 degrees Celsius. With respect to the thermal energy required for the
electrowinning process, this is matched by the exhaust gases mass flow that is found to
be around 15% at the inlet of the HRSG. These changes are the ones affecting the least
the overall performance of the system, thus promoting the optimum operational
management of the CHP system. Therefore, this location would be the most feasible and
viable location for assuring an easy installation process. Therefore, the exhaust gases
splitter system in the steam generator inlet is implemented. A summary of the main
geometric and operational features of the designed cogeneration plant are presented in
Table 4.3.
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Table 4.3. Cogeneration system operating parameters for full load gas turbine.
Component Value Heat exchanger (hot water) Exhaust gases mass flow (kg/s) 90 Exhaust gases inlet temperature (°C) 621 Water mass flow (kg/s) 278 Water inlet temperature (°C) 40 Global heat transfer coefficient (W/m2 K) 3,500 Global heat exchange surface (m2) 150 Pipeline (hot water) Pipe internal diameter (m) 0.508
Wall length (m) 0.03175
Thermal insulation thickness 0.120 Heat exchanger (electrolyte) Water mass flow (kg/s) 278 Water inlet temperature (°C) 90 Electrolyte mass flow (kg/s) 278 Electrolyte inlet temperature (°C) 27 Heat transfer coefficient for the hot side (W/m2 K) 7,250 Heat transfer coefficient for the cold side (W/m2 K) 1,800
The cogeneration plant design was implemented into the combined cycle power
plant simulation model, while the CHP system performance was evaluated for a power
plant decrease load change case study. The respective results comparisons were
performed against a reference model. In Figures 4.30 and 4.31, the exhaust gases flow
deviated from the cogeneration plant are shown and the relative impact on the mechanical
power profiles of a steam turbine is quantified accordingly.
119
Figure 4.34. Exhaust gases flow profiles for CCPP and CHP System.
Figure 4.35. Mechanical power profiles for CCPP and CHP System.
120
In order to supply thermal energy that is required by the electrowinning process,
around 15% of exhaust gases must be diverted from the cogeneration plant for the gas
turbine full load case. While equivalent mass flows of 20%, 19%, 18%, 17% and 16%
must be directed to the cogeneration plant for partial loads of 50%, 60%, 70%, 80% and
90% respectively. It was noted that in regard to the steam turbine mechanical power,
there is an average decrease of 5% and a maximum decrease of 17% per turbine stage
(HP, IP, and LP) for the cases considered. In contrast, the CHP system average
thermodynamic efficiency is 15% greater than the combined cycle power plant average
efficiency, increasing from 53% to 68%. In addition, the proposed design of the CHP
system causes an average decrease of 32,500 tons of carbon dioxide emissions per year
by replacing the diesel boiler that currently provides thermal energy to the electrowinning
process in the mining complex.
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5. Chapter Five Surrogate modeling 5.1 Introduction The flexible operation of a thermal power plant includes fast startups and frequent load
changes. Under these operating cycles, the thermal power plants continuously modify the
working fluid parameters such as steam temperatures and pressures. As a consequence,
thermal and mechanical stresses are induced. Therefore, during the synthesis of optimum
operating procedures, accurate albeit faster structural integrity evaluation and lifetime
consumption in critical components are instrumental towards effective and are more
computationally efficient operating procedures synthesis.
Structural integrity evaluation and lifetime consumption can be calculated using
rigorous models that consider complex geometries using Finite Element Methods (FEM)8.
However, solving such models is computationally costly and often time consuming. For
example, the structural integrity evaluation of a superheater takes around fifteen hours
using FEM on a computer with 2.2 GHz CPU and 8 RAM. Assuming that the optimization
problem of the operating procedure synthesis is solved through 1,000 iterations, the
whole structural integrity evaluation process would require about 625 days to run.
To minimize the time amount required to evaluate the critical component structural
integrity constraint during the optimization process, we propose the development of
surrogate models based on response surfaces and machine learning techniques. These
models can be used to estimate the thermomechanical stress distributions and lifetime
consumption. The surrogate model is generated from the results of a limited number of
simulations of a FEM model of the power plant superheater.
The FEM model has been developed so that, given an operating condition defined
by the pressure and temperature distributions in a time interval and for each critical
component of the power plant, the thermal and mechanical stress distributions are
determined in order to estimate the lifetime consumption for each operating condition.
8 Finite Element Method (FEM), which is a computational technique used to obtain approximate solutions of boundary value problems in engineering [151].
122
The FEM model was developed using the engineering simulation and 3D design
software Ansys Mechanical, which is a FEM modeling software for analyzing changes in
strength, toughness, elasticity, temperature and other properties of materials [151]. The
simulation structure is divided into three main sections or modules: pre-processor for
creating geometry and meshing, processor where the model is solved, and post-
processor where the results obtained are displayed and analyzed. This finite element
software is mainly used for the solution of mechanical problems such as dynamic and
static structural analysis (both for linear and non-linear problems), heat transfer analysis
and dynamic fluid, as well as problems of acoustics and electromagnetism [20]. It is
mainly used to predict how a certain product will work and respond under a real
environment.
The proposed surrogate model is generated from the results of finite element
simulations, which allow determining the stress distribution and helps to identify
susceptible failure zones in the power plant critical component under the effect of thermal
and mechanical loads. Thereafter, machine learning models (ML) were developed to
identify behavior patterns allowing estimating stress levels and consumption of useful life
using a minimum amount of information available in response surfaces. Artificial Neural
Networks (ANN) is proposed as a machine learning modeling approach.
123
5.2 The superheater As reported in Chapter 2, the most critical limiting factor for the synthesis of optimum
operating procedures of thermal power plants is the lifetime consumption of the
superheater caused by the thermal and mechanical stresses.
The steam superheater is a heat exchanger that produces superheated steam, in
which the wet steam is converted into dry steam using sensible heat to superheat the
steam in order to increase its enthalpy [152]. The gas turbine hot exhaust gases provide
the required temperature to produce superheated steam, thereby increasing the efficiency
of the steam power plant, minimizing the erosion of turbine blades and reducing the
condensation loss in the steam pipes [152]. In Figure 5.1, a 3D model of a typical power
plant superheater configuration is illustrated [153], in which the hot flue gas (gas turbine
exhaust gas) is shown in red, while cold streams (steam) are outlined as blue lines.
Figure 5.1. A superheater basic configuration [153].
124
Convection is the main mode of heat transfer mechanism between the flue gases
and the superheater. With an increase in steam demand, both fuel and airflow in gas
turbines increase, increasing flue-exhaust gas flow. As a result, convective heat transfer
coefficients increase both inside and outside the tubes [154].
During the operation of the power plant, there is superheated steam acting on the
internal surfaces of the superheater header, in which the pressure and temperature
distributions in the header are homogeneous and constant, and the magnitude of these
variables change according to the steam demand of the power plant.
5.3 Surrogate modeling The proposed surrogate model starts from a rigorous model based on the finite element
method. The superheater header model is validated against a FEM model of a header
available in the literature [80]. Then, a transient heat transfer analysis that simulates the
header heating process during power plant startup is carried out. From this analysis, the
effects of temperature and pressure changes on the structural integrity of the header are
quantified. It is confirmed that the temperature and stress distributions are homogeneous
and constant, changing only their magnitude and maintaining the location of the maximum
stress zones prone to failure for all cases of study. Therefore, unit load FEM models for
mechanical and thermal loads are proposed. The unit load FEM models and their
respective escalation according to the pressure and temperature profiles of the
superheated steam are compared against the transient analyses of the header, finding a
wide correlation both in the distributions and in magnitudes. Then a response surface
model for each kind of load is developed to visualize the behavior of failure-prone zones
of the header. Finally, based on the response surface models data an Artificial Neural
Networks (ANN) model is developed, which is validated against the results of the FEM
simulations. The superheater header surrogate model implementation flowchart is shown
in figure 5.2.
125
Figure 5.2. The superheater header surrogate model implementation flowchart.
126
The procedure of the generation of the surrogate model is organized as following:
1. The original model is evaluated at multiple sample points of temperature and
pressure, producing a number of simulation results.
2. A response surface model is developed to visualize the failure-prone zones of the
header.
3. After identifying the failure-prone zones, the original simulations in those zones are
used to generate an Artificial Neural Networks (ANN) model.
4. The ANN model is validated against the results of the FEM simulations.
The resulting ANN model is stored in a data file for later use in evaluating the header
structural integrity constraint in the dynamic optimization process using connection
interphase between the optimization framework and the ANN.
In order to generate the response surfaces of the failure-prone zones of the
superheater header, the following assumptions were taken into account:
Given that the superheater header operates in a superheated steam environment
in which the pressure and temperature distributions are considered uniform both
inside the cylinder and in the nozzle holes, the finite element reference simulations
used to develop the surrogate model are performed using unit thermal and
mechanical loads.
Since the maximum stresses for each load are located in different zones of nozzles holes, the thermal and mechanical stress distribution are to be individually
processed and scaled based on its real operating loads.
The effects of thermal and mechanical loads will be integrated using the superposition method9 once each of these loads has been individually scaled.
The failure prone zones are considered as the critical zones of the header for the
generation of response surface models.
The superheater header rigorous finite element model includes the geometric and
operational features shown in Table 5.1 and was validated against the model of Yasniy
[80].
9 The superposition method consists of obtaining stresses as linear combination of the individual loads.
127
Table 5.1. Superheater header features.
Parameter Value
Header type (cold, hot) Hot
External header diameter, m 0.325
Thickness, mm 0.050
Place of template cut (distance from the end cap of the header), m 3.45
Steel grade 12CrMoV
Internal pressure during operation 15.5 MPa
Operational temperature (external and internal walls) 545 °C internal
565 °C external
Yield strength 320 MPa
Ultimate strength 480 MPa
Considering the header symmetry conditions, only a quarter section of the
superheater header was used in FEM analysis. The finite element mesh was refined in
the vicinity of the holes. The total number of elements used in the model was 569,280.
Based on the results reported by Roy et al. [165], Kwon et al. [166], Morgan and Tilley
[167], and Yasniy et al. [168], in which they identify that the region’s most prone to
operational damage and defects are the ligaments between the holes of nozzles
supplying superheated steam. Our numerical model was refined in the vicinity of nozzles
holes with minimal spacing between the finite element nodes of 0.025 mm, as shown in
Figure 5.3.
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Figure 5.3. Finite element model of the superheater header with mesh refinement in the vicinity of nozzles holes.
To quantify the effects of the thermal load on the header, initially, a heat transfer
analysis must be carried out, and from this transfer the temperature distributions on the
header to the structural module of Ansys Workbench in order to determine the stress
distribution by thermal loads. In the same way, the mechanical load caused by the
pressure of the superheated steam in the header inner surfaces is evaluated from a
structural static analysis at power plant full load.
To carry out the header heat transfer analysis, the thermal boundary conditions
must be calculated, which are determined by the convection heat transfer coefficients
[80]. In this context, a natural convection is modeled on the header external surfaces,
while forced steam convection is modeled on the header internal surfaces.
The heat transfer coefficients for the superheater header cylinder and nozzles
holes zones are computed according to the following equation [60]:
ℎ𝑐 = 𝑁𝑢 ∙𝑘
𝑑ℎ𝑦𝑑 (5.1)
where ℎ𝑐 the steam-side convection coefficient, 𝑘 is the fluid thermal conductivity
and 𝑑ℎ𝑦𝑑 is the hydraulic diameter of the pipe. 𝑁𝑢 is the average Nusselt number, which
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is computed using Reynolds number using an equation put forward by Gnielinski [169]
for heat transfer during the turbulent flow of gases and liquids through pipes [135].
𝑁𝑢 =(0.125𝜉) ∙ 𝑃𝑟 ∙ 𝑅𝑒
1 + 12.7 ∙ √0.125𝜉 ∙ (𝑃𝑟23 − 1)
∙ [1 + (𝑑𝑖𝑙)
23
] (5.2)
Where 𝑃𝑟 and 𝑅𝑒 are the Prandtl number and the Reynolds number, respectively;
𝑙 is the pipe length and 𝑑𝑖 is the pipe inner diameter, while the friction factor 𝜉 is given by
the next equation [170]:
𝜉 = (1.8 ∙ log10(𝑅𝑒) − 1.5)−2 (5.3)
According to data provided by Farragher et al. [60] and taking into account the
recommendation of average velocity to prevent significant pressure drop in long steam
pipe lengths by [171], the steam velocity is taken to be 15 m/s. In order to have a match
on predicted outer header surface temperature, the external convection heat transfer
coefficient is established as ℎ𝑜 = 1900 𝑊 𝑚2𝐾⁄ . The resulting convection heat transfer
coefficients values for the header inner surfaces are tabulated in Table 5.2.
Table 5.2. Header convection heat transfer coefficients.
Header zones (internal surfaces) 𝒉𝒊(𝑾 𝒎𝟐𝑲⁄ )
Thick-walled cylinder 4,750
Nozzle holes 3,980
The boundary conditions for the heat transfer analysis are shown in figures 5.4 to 5.5.
Likewise, the header temperature distribution for the FEM heat transfer analysis is shown
in Figure 5.6. Regarding mechanical stress analysis, a pressure equivalent to
superheated steam pressure in the inner cylinder and nozzles holes surfaces of the
header is imposed, as shown in Figure 5.7. Likewise, the field of normal von Mises
stresses due to thermal and mechanical loads, as well as the critical failure-prone zones,
are shown in Figures 5.8 and 5.9.
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Figure 5.4. Heat transfer boundary conditions in the superheater header nozzle’s holes and inner surfaces.
Figure 5.5. Heat transfer boundary conditions in the external surfaces.
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Figure 5.6. Header temperature distribution for the FEM heat transfer analysis.
Figure 5.7. Mechanical load in terms of pressure on the inner cylinder and on the surfaces of the nozzle holes of the header.
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Figure 5.8. Normal von Mises stress distribution in the header under unit thermal load.
133
Figure 5.9. Normal von Mises stress distribution in the header under unit mechanical load.
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From the results of the unit load simulations, it can be seen that the von Mises stress and
temperature distributions have the same pattern as those of the reference model [80] with
a difference of 0.7383% in the von Mises stresses for models with the same mesh quality.
As expected, the magnitude of these variables is different for each header case study.
Also, to verify if the stress and temperature distributions in the header change according
to the steam demand of the power plant, dynamic simulation analyses are carried out.
5.3.1 Dynamic header behavior based on unit FEM static models To determine the transient state behavior of the header, a header heating process is
simulated that resembles a power plant startup process, in which the state variables
characteristic of superheated steam, such as the pressure and temperature of the steam
inside the header changes over time. The header heating curve in terms of the steam
pressures and temperatures for the transient analysis is shown in Figure 5.10, in which
the temperatures and pressures increase from an initial state to environmental conditions
until reaching their desired final state around 3650 seconds, remaining in its desired final
state until simulation end. In this figure, the blue and red curves represent the
temperatures in the cylinder inner surfaces and nozzle holes inner surfaces of the header,
respectively. The green line shows the evolution of the pressure inside the header during
the transient state analysis. The boundary conditions, load distributions and symmetry
regions have the same configurations as those used in the full and unit load finite element
analysis.
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Figure 5.10. Thermal and mechanical load curve in terms of the steam pressures and temperatures for the transient analysis.
From the heat transfer transient analysis, the temperature distributions in the
superheater header for each evaluation time are obtained. In Figure 511, the temperature
evolution in the inner and outer surfaces of the header during heat transfer transient
analysis is shown. The temperatures inside and outside the superheater increase from
an initial state to environmental conditions until reaching their desired final state around
3650 seconds, remaining in its desired final state until simulation end.
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Figure 5.11. Temperature evolution in the inner and outer surfaces of the header during heat transfer transient analysis.
The header temperature distributions from transient heat transfer analysis are used
as thermal loads in a transient structural analysis to calculate the stresses induced by the
thermal load in the header. Likewise, the changes in the internal pressure of the header
are used as a mechanical load to determine the header stresses through a transient
structural analysis. Figure 5.12 shows the evolution of thermal and mechanical stresses
in the header.
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Figure 5.12. Thermal and mechanical stresses evolution in the header for structural transient analysis.
In the same way, to illustrate the stress distribution patterns trends obtained in the
transient analysis, a comparison of the thermal and mechanical stress distributions is
carried out at selected points of the transient analysis against the thermal and mechanical
stress distributions of the unit load static analysis. The comparisons of thermal stresses
are shown in Figure 5.13 and 5.14, in which a correlation is observed between the stress
distributions for the unit static analysis in the upper left part of both figures and the stress
distributions in the header for different simulation times in the others parts of the Figures
5.15 and 5.16. Regarding the behavior of mechanical stresses, these are shown in
Figures 5.15 and 5.16. Likewise, there is a correlation between the stress distributions for
the unit static analysis shown in the upper left and the mechanical stress distributions in
the header for different times in transient analysis as is illustrated in Figures 5.15 and
5.16. A comparative of the evolution of the header thermal and mechanical stresses over
time using transient structural analyses and their corresponding stresses escalation
based on the unit static analyses results are presented in Figures 5.17 and 5.18.
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Figure 5.13. Comparison of thermal stresses distributions between the unit static analysis and some simulation times at the beginning of the transient analysis.
139
Figure 5.14. Comparison of thermal stresses distributions between the unit static analysis and some simulation times at the end of the transient analysis.
140
Figure 5.15. Comparison of mechanical stresses distributions between the unit static analysis and some simulation times at the beginning of the transient analysis.
141
Figure 5.16. Comparison of mechanical stresses distributions between the unit static analysis and some simulation times at the end of the transient analysis.
142
Figure 5.17. Thermal stresses evolution in the header. A comparison is made between structural transient analysis and their corresponding stresses escalation based on the unit static analysis.
Figure 5.18. Mechanical stresses evolution in the header. A comparison is made between structural transient analysis and their corresponding stresses escalation based on the unit static analysis.
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From the results in the static and transient numerical simulations of the header, we
can conclude the following:
– There is an excellent agreement in the distribution patterns of thermal and
mechanical stresses between the static analyses and their corresponding
transients’ analyses, as shown in Figures 5.13 to 5.16.
– The most stressed zones for both thermal and mechanical loads are in the nozzle
holes. However, the header failure-prone zones for both load cases are at
different radial positions of the nozzles. For the thermal load case, the failure-
prone zone is in the plane XY of the nozzle holes. While the failure-prone zone
for the mechanical load case is in the plane ZY of the nozzle holes.
– In the heating header transient analysis, which is analogous to the power plant
startup, the maximum stress for thermal and mechanical load cases appear at
different times. Therefore, they are not directly cumulative.
– The maximum stresses for both the static analyses and their corresponding
transients’ analyses are in the same place. Therefore, the structural integrity of
the header can be quantified evaluating the critical zone of the header in the
nozzle holes.
– From the stress distribution comparisons for the static and transient analyzes in
Figures 5.13 to 5.16, it can be seen that they have similar distribution patterns
and only differ in magnitude. Therefore, the stress distribution in the header can
be obtained by scaling the results of the static analysis of the unit according to
the pressure and temperature differentials of the load case that will be analyzed
as shown in Figures 5.17 and 5.18.
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5.3.2 Response surface models Response-surface models were generated to visualize the failure-prone zones. The
response-surface models were created using 5,945 nodes of the finite element numerical
model, representing about 1.05% of the total information contained in the full finite
element model of the superheater header.
The failure-prone critical zone in the header can be seen in Figure 5.19. The
corresponding response surfaces for each unit load case in the critical zone of the
superheater header are shown in Figures 5.20 and 5.21.
Figure 5.19. Failure-prone critical zone in the header.
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Figure 5.20. Header stress response surface under unit thermal load.
Figure 5.21. Header stress response surface under unit mechanical load.
146
Once the response surfaces of the critical zone have been generated, the thermal and
mechanical stress distribution will be individually processed and scaled based on the
operational data of the component obtained from the dynamic simulation model of the
power plant, that is, the header differential pressures and temperatures differentials for
each simulation time. Then, the effects of thermal and mechanical loads will be integrated
using the superposition method.
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Figure 5.22. Response surface scaled according to the pressure differential in the header.
148
Figure 5.23. Response surface scaled according to the header differential temperature.
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5.3.3 Artificial Neural Networks (ANN) model
Artificial Neural Networks (ANN) are models inspired by the central nervous system,
which are made of interconnected neurons [155]. One of the most common type of ANN
is the Multi-Layer Perceptron (MLP). An MLP artificial neural network is composed of
multiple layers of neurons: an input layer, one or more hidden layers, and an output layer.
The input layer is responsible for receiving a given input vector and transform it into an
output that becomes the input for another layer. A hidden layer transforms the output from
the previous layer through a transfer function. Each neuron has an activation function
(also known as transfer function) that receives the input from all the neurons in the
preceding layer, multiplies each input by its corresponding weight vector and then adds
a bias. Considering the rule described in HeatonHL [156] and then updated in
heatonHLAct [157], which recommended three or more layers for complex problems as
a prediction or computer vision. In this work, a three-hidden layer with 19 neurons in the
first layer, 17 neurons in the second layer, and 15 neurons in the third layer ANN were
implemented. The selected number of neurons per hidden layer was a result of testing
different numbers from 20 neurons per hidden layer and below. Each neuron of the neural
network represents a node. Nodes are elements that help the neural network to model
the behavior of a certain phenomenon, however, nodes have not a direct relationship with
the phenomenon the artificial neural network is modeling.
The method for training the ANN models is the Resilient Backpropagation Method
described by Riedmiller and Rprop [158]. In this thesis, the sigmoidal function is used as
activation function [159]. In Figure 5.24, a graphical representation of this ANN
configuration is shown.
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Figure 5.24. Graphical representation of the configuration of the neural net model.
The training steps for the proposed ANN are the following:
– First, the data was changed from wide to long format, so we have every point
represented by its coordinates X and Y.
– Then, the data in long format was ordered according to the X coordinate for the
mechanical stress, and according to the Y coordinate for the thermal stress.
– Then, from the ordered data was selected 20% of the first and 20% of the last
elements of the data. The rest of the data was used for testing.
– Finally, the ANN model was trained with the selected training data and the trained
model was tested using the rest of the data.
The ANN model input consisted of geometric positions of the failure-prone zones (𝐿),
determined by the axial (𝑍) and radial (𝑌) coordinates of the header; and an binary
variable (𝑠), that distinguishes the kind of stress (𝑠 = 0) for thermal load and (𝑠 = 1) for
mechanical load. The output of the artificial neural network model was the corresponding
stress, 𝑇𝑆 for thermal stress and 𝑀𝑆 for mechanical stress. As shown in Table 5.3, each
sampling point 𝑖 consists of 𝑛 groups of parameters values, where each group is
organized as (𝐿𝑖𝑗 , 𝑌𝑖 , 𝑍𝑖, 𝑠) with output 𝑇𝑆𝑖𝑗 and 𝑀𝑆𝑖𝑗, where 𝑛 represents the number of
points for each response surface model.
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Table 5.3. Structure of the inputs and outputs for ANN model.
Inputs Outputs
𝑳 𝒀 𝒁 𝒔 𝑻𝑺 𝑴𝑺 𝑳𝟏𝟏 𝒀𝟏 𝒁𝟏 0 𝑺𝑻𝟏𝟏 0
𝑳𝟏𝟏 𝒀𝟏 𝒁𝟏 1 0 𝑴𝑺𝟏𝟏
⋮ ⋮ ⋮ ⋮ ⋮ ⋮
𝑳𝒎 𝒀𝒎 𝒁𝒎 0 𝑺𝑻𝒎 0
𝑳𝒎 𝒀𝒎 𝒁𝒎 1 0 𝑴𝑺𝒎
The proposed neural network model was validated against the thermal and
mechanical response surfaces. The accuracy measures were used to calculate the
discrepancy between the stress values calculated with the ANN model and the values
from the response surfaces. Specifically, the Mean Absolute Error (MAE), and Root Mean
Squared Error (RMSE) were used as accuracy measures (Table 5.4).
Table 5.4. Accuracy of the ANN model for the evaluation of the structural integrity constraint in the superheater header.
Training Test Complete Data
MAE 0.1753373 MPa 0.1751808 MPa 0.4584412 MPa
RMSE 0.2367 MPa 0.2363 MPa 0.8772 MPa
The MAE is the average mean absolute error of the neural network expressed in the
units of the original data, and RMSE is the average root mean square error of the neural
network expressed in the units of the original data. Mean Absolute Error represents the
precision of the model (the Artificial Neural Network). Root Mean Squared Error
represents a notion of big errors gets by the model. Both metrics were evaluated in the
Training and the Test data set and the model returned very similar results. However, also
both metrics were tested in the whole dataset (where the whole data set is the complete
geometry of stress), and also MAE and RMSE result was not significantly high with
respect of the Test and Training dataset, thus demonstrating consistency on the results
of the prediction model. Meanwhile, the training refers to the data set with the neural
network was trained (20% of the first and 20% of the last elements of the data), the test
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is a data set that is not known to the neural network (60 percent of the remaining data)
and complete data represents the full response surfaces data set generated through the
finite element simulations.
Regarding the computation time for the evaluation of stresses in the header, the
artificial neural network model and the response surfaces model have equivalent
processing times since, for both models, the same process must be carried out. The
process is as follows: each point of the model must be individually scaled according to
the pressure and temperature profiles for each simulation proposed by the optimization
algorithm. Then, the thermomechanical stresses in the header are determined, combining
the thermal and mechanical stresses calculated by the stress evaluation models using
the superposition method. On average, to assess the header structural integrity constraint
during the optimization process using these models, it takes 6.8 seconds for the ANN
model and 24 seconds for the response surface model.
The neural network model provides a continuous model; thus, it can provide results
given any point of interest. While the response surface model is a discrete representation
limited by the discretization of the header in the finite element model. In this way, if a point
of interest is needed other than the ones originally provided to generate the model it will
not be possible to get a result using a response surface model. Also, for elements with
similar geometries such as the boiler dome, a surrogate model based on artificial neural
networks can be generated from FEM models with coarse meshes and reduce the
amount of data to process, obtaining a good enough correlation of results, thereby
speeding up the evaluation process of the structural integrity of critical components of
thermal power plants in dynamic optimization processes.
The results in Table 5.4 suggest that the trained model is capable of reproducing with
high accuracy the complete data set using 40% of the original data. Also, the three MAE,
MAPE and RMSE errors are similar in magnitude.
Figures 5.25 and 5.26 show the graphical representation of the neural network model
for the thermal and mechanical response surfaces.
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Figure 5.25. Graphical representation of the neural network model of the thermal response surface.
Figure 5.26. Graphical representation of the neural network model of the mechanical response surface.
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5.3.3.1 Interface with the optimization algorithm After the optimization algorithm generates a given operating this operating procedure is
simulated, producing file that contains the pressure and temperature profiles of the steam
in the superheater. The pressure and temperature at each simulation time, the thermal
and mechanical stresses are calculated with the ANN models. Then, the
thermomechanical stresses in the header are determined, combining the thermal and
mechanical stresses calculated by the ANN models using the superposition method.
Subsequently, the maximum values of thermomechanical stress for each simulation time
are sent back to the optimization algorithm.
The structural integrity constraint evaluation in the dynamic optimization problem
for the synthesis of optimum operating procedures of thermal power plants using rigorous
finite element model requires around 15 hours for each proposed operation profile by the
optimization algorithm, while this same process is performed in 24 seconds for the
response surface model and 6.8 seconds for the surrogate model based on an artificial
neural network.
Comparison of times required to assess the structural integrity constraint in the
dynamic optimization problem for the synthesis of optimum operating procedures of
thermal power plants using rigorous finite element models, as well as using the response
surface models and an artificial neural network model is shown in Table 5.5 and Figure
5.27.
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Table 5.5. Comparison of times to assess the structural integrity constraint in the dynamic optimization problem using different models.
Figure 5.277. Comparison of times in minutes to assess the structural integrity constraint in the dynamic optimization problem using different models.
156
6. Chapter Six In this chapter, we evaluate the performance of the proposed approach with two case
studies. The first case study focuses on managing the thermal power plant's flexible
operation based on the synthesis of the startup operating procedure of a drum boiler. The
second case study addresses the synthesis of an optimum operating strategy of a
combined heat and power system to improve the electric power system’s operational
flexibility.
6.1 Case study 1: Synthesis of the startup operating procedure of a drum boiler
According to the literature review addressed in Chapter 2, achieving the flexible operation
of a thermal power plant can be carried using a process level approach as a first step in
the operational optimization of the entire power plant. Since steam generation is one of
the most important processes for the efficient operation of thermal power plants and that
the drum boiler startup time is considered the most critical element in the steam
generation process. This case study evaluates the proposed approach with the synthesis
of a startup operating procedure of a drum boiler, which aims at finding the optimal
sequences of control valves that minimize the drum boiler startup time.
As described in Chapter 3, two metaheuristic optimization algorithms were
implemented on the dynamic optimization framework, namely, a micro genetic algorithm
(mGA) and a hybrid algorithm based on simulated annealing and tabu search (SATAS).
As explained in Chapter 4, the simulation model of the drum boiler was validated by
executing the startup operating procedure published by Belkhir et al. [98] and comparing
the pressure, temperature, thermal stress, heat supplied, and steam flow regulation
profiles.
The dynamic optimization problem of the drum-boiler startup aims at achieving a
given state in terms of the drum-boiler internal pressure and the output steam mass flow
rate, in the shortest time possible, while avoiding excessive thermal stresses. Therefore,
the formulation of the optimization problem for the startup operating procedure can be
written as follows:
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Objective function:
min∑𝑑𝑡 + 𝜔1[𝑝(𝑡𝑓) − 𝑝𝑔𝑜𝑎𝑙]2+𝜔2[𝑞(𝑡𝑓) − 𝑞𝑔𝑜𝑎𝑙]
2 (6.1)
𝑡𝑓
𝑡𝑜
where 𝑝𝑔𝑜𝑎𝑙 is the desired internal pressure, 𝑞𝑔𝑜𝑎𝑙 is the desired steam mass-flow
rate, and 𝜔1 and 𝜔2 are the weights. Based on Belkhir et al. [98], the desired internal
pressure and the desired steam mass-flow rate were set to 90 bar and 185 kg/s,
respectively, while 𝜔1 and 𝜔2 were set to 0.01 and 0.001, respectively. Model constraints
must be fulfilled any time during the optimization horizon 𝑡 ∈ [𝑡0, 𝑡𝑓]. The internal pressure
and the steam mass-flowrate are controlled by regulating the heat flow at the input of the
drum boiler and the output flow rate of the steam that is extracted from the drum boiler.
However, the input heat flow cannot exceed 500 MW.
0 ≤ 𝑄 ≤ 500 𝑀𝑊 (6.2)
In addition, the position of the steam valve is assumed to take discrete values
between 0 and 1.
0 ≤ 𝑉𝑝𝑜𝑠 ≤ 1 (6.3)
In order to avoid sudden changes in the state variables, the heat flow rate (𝑑𝑄 𝑑𝑡⁄ ) is
constrained as follows:
0 𝑀𝑊
𝑚𝑖𝑛≤𝑑𝑄
𝑑𝑡≤ 25
𝑀𝑊
𝑚𝑖𝑛 (6.4)
In the same way, a feasible solution must be able to achieve the objective by fulfilling
the process constraints. In this context, we set up inequalities constraints that determined
the state variables operational range such as temperature and pressure inside the drum
boiler:
𝑝(𝑡𝑓)𝑚𝑖𝑛< 𝑝(𝑡𝑓) < 𝑝(𝑡𝑓)𝑚𝑎𝑥
(6.5)
𝑇(𝑡𝑓)𝑚𝑖𝑛 < 𝑇(𝑡𝑓) < 𝑇(𝑡𝑓)𝑚𝑎𝑥 (6.6)
These inequalities set the state variables limits and the mix quality in the drum boiler,
for which it must be fulfilled that 𝑝(𝑡𝑓)𝑚𝑖𝑛 ≥ 𝑝𝑎𝑡𝑚 , 𝑝(𝑡𝑓)𝑚𝑎𝑥 ≥ 𝑝𝑛𝑜𝑚 , 𝑇(𝑡𝑓)𝑚𝑖𝑛 ≥ 𝑇𝑒𝑐𝑜 and
158
𝑇(𝑡𝑓)𝑚𝑎𝑥 ≥ 𝑇𝑛𝑜𝑚, where, 𝑝𝑎𝑡𝑚 is the atmospheric pressure, 𝑇𝑒𝑐𝑜 is the temperature in the
economizer, 𝑝𝑛𝑜𝑚 is the full load nominal pressure, and 𝑇𝑛𝑜𝑚 is the full load nominal temperature.
Moreover, large thermal stresses must be avoided in the drum boiler thick wall.
−10𝑁
𝑚𝑚2≤ 𝜎𝑉𝑀 ≤ 10
𝑁
𝑚𝑚2 (6.7)
As explained in Chapter 3, the same data structure was used in both metaheuristic
optimization algorithms. The solution is represented by three chromosomes. The first
chromosome represents the sequence of actions. The second chromosome represents
the execution time per action, and the third chromosome represents the number of times
that the pair (action, execution time) is repeated. Each element in the first chromosome
is an integer that points to a combination of the valve position of the steam outlet valve
and the heat flow rate. Table 6.1 shows the set of actions considered for this problem as
a combining discrete value of the heat flow rate and the steam flow rate.
Table 6.1. Combinations of the heat flow rate and steam flow rate for each action.
Action Heat Flow Rate [MW/min]
Valve Position
1 8 0.0 2 8 0.6 3 8 1.0 4 16 0.0 5 16 0.6 6 16 1.0 7 24 0.0 8 24 0.6 9 24 1.0
The experiments considered three action durations (60, 120, and 180 s) and three-valve
positions (valve completely closed, valve 60% open, and valve completely open). As a
result, eight different actions were obtained, resulting from the combination of three valve
positions for the two valves (the case of both valves closed was not considered).
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The repetition parameter was set to take integer values from 0 to 10. The length of
the sequence is fixed to 9 elements.
The mGA probabilities used in the numerical experiments were 10% for mutation and
20% for crossover. The population of the mGA consisted of 5 individuals, and the
termination criteria were set to a maximum of 40 generations and 20 epochs, respectively.
The SATAS algorithm was initiated with a randomly generated solution and the
termination criteria were set to 1,000 iterations. The optimization process of the SATAS
algorithm generates new solutions through the neighborhood operator (NOP). The NOP
takes an existing solution and randomly changes one of the sequences (operator, time,
and repetition).
All the experiments were carried out on a 3.4 GHz Intel Xeon E3-1245 V2 computer
with 16 GB of RAM, running Windows 10 pro.
Figure 6.1 shows the distance from the current state to the goal state throughout the
simulation, that is, how the characteristic state variables of the objective function getting
closer to their desired state for both optimization algorithms, mGA, and SATAS. The
results of the mGA algorithm are shown in dotted lines, while the results obtained with
the SATA algorithm are illustrated with solid lines. From these results, it can be seen that
the SATAS algorithm reaches the desired state by 7% less time than the mGA algorithm.
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Figure 6.1. Comparison of the distance from the current state to the goal state overtime for the drum boiler startup optimization obtained with mGA (dotted lines) and SATAS (solid lines).
Figures 6.2 to 6.9 show the comparison of the results of this research with those
obtained by Åström & Bell [105], Franke et al. [95], and Belkhir et al. [98]. In these figures,
red lines correspond to the Åström & Bell model, while the green and gray lines are the
results presented by Franke et al. and Belkhir et al., who solved the optimization problem
using a nonlinear model predictive control (NMPC) and the interior point method (IPOPT),
respectively. The black and blue lines correspond to the optimized drum boiler startup
profile according to the dynamic optimization framework proposed in this research using
mGA and SATAS algorithms respectively.
Figure 6.2 shows the maximum power generated during the startup process. Figures
6.3 and 6.4 show the comparison of the operating profiles of the internal pressure and
the steam mass-flow rate. Figures 6.5 to 6.8 show the operation of the valves that control
the heat supplied to the system and the steam flow that is sent to the power train. Finally,
the system structural constraint profiles are shown in Figures 6.9.
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Figure 6.2. Results comparison between the curves of the operating benchmark profile developed by Åström & Bell, the optimized profiles reported by Franke et al. and Belkhir et al., and the proposed approach mGa and SATAS for the power generated.
Figure 6.3. Results comparison between the curves of the operating benchmark profile developed by Åström & Bell, the optimized profiles reported by Franke et al. and Belkhir et al., and the proposed approach mGa and SATAS for the steam that exits of the system.
162
Figure 6.4. Results comparison between the curves of the operating benchmark profile developed by Åström & Bell, the optimized profiles reported by Franke et al. and Belkhir et al., and the proposed approach mGa and SATAS for the pressure in the drum boiler.
For the power generated (Figure 6.2) and the state variables (Figures 6.3 and 6.4), it
can be observed that the mGa algorithm can achieve the desired startup goal in less time
than previous works with a small number of iterations in the mGA optimization algorithm.
Meanwhile, the SATAS algorithm can achieve the desired startup goal in less time than
the benchmark model developed by Åström & Bell [105] and the optimized profiles
reported Franke et al. [95] and Belkhir et al. Likewise, the proposed framework using both
algorithms was capable of generating the sequence of valve operations of the steam
regulation valve and the heat flow supplied to the system, which was the main controlled
process variables that determine the efficiency of the steam generation process in a
thermal power plant.
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Figure 6.5. Results comparison of the operating profile of the steam regulating valve between the models Åström & Bell, Franke et al. and Belkhir et al.
Figure 6.6. Results comparison of the optimized operating profile of the steam regulating valve based on the proposed approach using mGa and SATAS algorithms.
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Figure 6.7. Results comparison of the operating profile of the heat flow supplied to the system between the models Åström & Bell, Franke et al., and Belkhir et al.
Figure 6.8. Results comparison of the optimized operating profile of the heat flow supplied to the system based on the proposed approach using mGa and SATAS algorithms.
As shown in Figure 6.5, the saturated steam regulation valve that supplied energy to
the powertrain remained fully open during the entire startup process for the model
developed by Åström & Bell [105], while for the optimized profile presented by Franke et
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al. [95], the steam flow regulation was carried out from 1000 to 1400 s, displaying large
instabilities in the state variables. Regarding the profile optimization reported by Belkhir
et al. [98], the steam valve regulation was minimal, since the valve changes ranged from
fully open to 98% and 99% open, with instabilities in the state variables. In contrast, the
proposed dynamic optimization framework suggests for both optimization algorithms that
the steam flow control valve should be operated sequentially and gradually in order to
achieve the goal state efficiently, generating stable and continuous profiles for the state
variables.
In the same way, the heat supply for the Åström & Bell [105] model was carried out
continuously and constantly from the beginning of the process until the system reached
the goal state. For the profiles proposed by Franke et al. [95] and Belkhir et al. [98], the
heat supply was achieved by oscillating and intermittent patterns. In the case of the
proposed framework, the heat supply is continuously applied and gradually increased
until the goal state reached for both optimization algorithms. The heat supply profiles of
the system for all startup processes evaluated in this paper are shown in Figures 6.7 and
6.8.
Figure 6.9. Results comparison between the curves of the operating benchmark profile developed by Åström & Bell, the optimized profiles reported by Franke et al. and Belkhir et al., and the proposed approach mGa and SATAS for the thick-walled von Mises stress.
.
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Finally, to avoid hazardous scenarios in which the proposed profiles could result in a
decrease of useful life and the structural integrity of the thick-walled components
constraint must be monitored.
Table 6.2 shows a comparison of the thermal useful life consumption and fatigue
damage in the drum boiler for all startup profiles evaluated in this case study. The useful
life estimation was carried out based on the model proposed by Živković et al. [175], using
the rainflow cycle counting method reported by the ASTM E 1049 Standard [75] and
considering the 200 minimum startup cycles recommended for the efficient and safe
operation of a thermal power plant by Ruchti et al [27]. Meanwhile that the thermal
cumulative damage in the drum boiler was carried out using the Palmgren-Miner Rule
[176].
Table 6.2. Comparison of the useful life consumption and fatigue damage in the drum boiler for all startup profiles evaluated in the case study 1.
Model Damage [%] Increase in life consumption [%] Residual life [%]
Åström & Bell [105] 15.49 0.00 84.51
Franke et al. [95] 38.34 22.85 61.66
Belkhir et al. [98] 36.19 20.70 63.81
mGA 18.53 3.04 81.47
SATAS 18.04 2.55 81.96 In this context, in the case of the optimized profiles presented by Franke et al. [95]
and Belkhir et al. [98], there is an increase in fatigue damage of about 1.5 times against
to the benchmark profile presented by Åström & Bell [105], since more alternating tension
and compression stresses occur, with higher magnitudes. In contrast, the profiles
generated by the proposed dynamic optimization algorithms minimize the drum boiler
startup time by 35% for the mGA algorithm and 42% for the SATAS algorithm with a
decrease in the useful life of 3 and 2.5 percent respectively compared to the Åström &
Bell [105] benchmark model.
In summary, the proposed dynamic optimization framework is capable of designing
the operation sequence that minimized the drum boiler startup times to satisfy the steam
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demand required by the power plant, identifying the corresponding control actions and
their sequence in order to design integrally the optimal operating procedure, without
compromising the structural integrity of critical components. Likewise, a scalable tool was
developed focused on being implemented in more complex processes and applications,
whose applications involved advanced dynamic simulation and optimization techniques
aimed at improving the designs of the operating procedures.
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6.2 Case study 2: Synthesis of an optimum operating strategy of a CHP system
As described in Chapter 2, the power system operational flexibility can be managed using
a power plant level approach, which focuses on the minimization of the operating times
and the maximization of the system’s capabilities to work under cyclic operating
conditions without compromising the structural integrity of power plant critical
components. In this context, a case study that focuses on the synthesis of an optimum
operating strategy of a combined heat and power system to increase its operational
flexibility is presented.
This case study focuses on the operation of steam turbines to improve the operational
flexibility of a power plant, for the electrical power generation and thermal energy
production required by a mining process.
For this case study, the proposed dynamic optimization framework described in
Chapter 3 and the surrogate model described in Chapter 5 that estimates in a
computationally efficient way the structural integrity is coupled to solve the operating
procedure synthesis problem for a combined heat and power system.
This case study uses the simulated annealing and tabu search (SATAS) optimization
algorithm since it provided the best results as shown in case study 1 of this Chapter. The
Combined Cycle Power Plant (CCPP) simulation model was validated against the load
change scenario published by Hefni and Bouskela [52]. The gas turbine mechanical
power, steam turbines mechanical power, gas turbine exhaust gas temperature, and
drums boiler levels were compared, obtaining consistent results with negligible numerical
differences as explained in Chapter 4. The simulation model in this case study reuses the
CCPP model, adjusting the mechanical power of the gas turbine according to operational
data of the San Isidro II power plant operating in Chile and the electrowinning plant that
is supplied with process heat corresponding to a copper mining installation present and
operating in Chile as explained in Chapter 4. Finally, the proposed surrogate model of the
superheater based on finite element simulations, response surfaces, and an Artificial
Neural Networks model (ANN) is used to estimate in a computationally efficient way the
structural integrity constraint of the dynamic optimization problem.
The synthesis of the optimum operating strategy of the combined heat and power
system is addressed as a dynamic optimization problem, in which the aims to supply
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thermal energy to selected electrowinning process and achieving a given state in terms
of the pressure and temperature of the steam in the high-pressure superheater, and
steam turbine power, in the shortest time possible, while avoiding excessive
thermomechanical stresses.
In order to investigate the demand patterns of the CHP system for this case study,
historical operational data of the San Isidro II combined cycle power plant [12] were
evaluated, as well as the thermal energy requirements of the electrowinning process
[149]. As shown in Figure 10, the power plant mostly operates under repetitive trends and
patterns of cyclic operation. After analyzing these data, it was possible to identify that a
typical operating cycle starts with a load at baseload, passing to a partial load in periods
of low demand, to finally return to operate at baseload at times linked to the periods of
greatest demand from the electricity grid (baseload-minimum-load-baseload).
Figure 6.10. Steam turbines operational data of the San Isidro II combined cycle power plant for the 2018 year.
On the other hand, the electrowinning process of copper mining requires a continuous
supply of thermal energy.
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In this case study, the operation of the power plant steam turbines and the thermal
energy generation for the mining process are managed through a splitter system of the
gas turbine exhaust gases. At the beginning of the cyclic operation case study, steam
turbines are generating electrical power at baseload, while the cogeneration system is
not under operation. Once the steam turbine operation moves towards the minimum load,
the cogeneration system begins the generation process of thermal energy for the
electrowinning process. When the steam turbines reach their minimum load state, the
cogeneration system must be reaching the thermal energy production required by the
electrowinning process. The next stage of the cyclic operation case study consists of the
steam turbines changing their load toward a new baseload since some amount of gas
turbine exhaust gas is used to generate the thermal energy of the mining process. In this
stage, we seek to increase the operational flexibility of the CHP system by implementing
the proposed dynamic optimization framework coupled with the developed surrogate
model, to produce operating procedures that minimize the time needed to take the power
plant from an initial state (minimum load) to the goal state (baseload) along with their
corresponding sequence of control valves operations without compromising the structural
integrity of critical plant components. At the same time, the gas turbine exhaust gases
must be controlled to keep a stable and continuous generation of thermal energy for the
mining process. Figure 6.11 shows the operating scheme to be developed by the power
plant and the electrowinning process during the cyclic operation case study for the CHP
system.
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Figure 6.11. Normalized operating scheme of the CHP system during the cyclic operation case study.
The formulation of the dynamic optimization problem for the cyclic operating
procedure of the CHP system can be written as follows:
Objective function:
min∑𝑑𝑡 + 𝛼[𝑝𝑒𝑣𝑎(𝑡𝑓) − 𝑝𝑔𝑜𝑎𝑙]2+ 𝛽[𝑇𝑒𝑣𝑎(𝑡𝑓) − 𝑇𝑔𝑜𝑎𝑙]
2+ 𝛾[𝑊𝑆𝑇(𝑡𝑓) −𝑊𝑔𝑜𝑎𝑙]
2
𝑡𝑓
𝑡𝑜
(6.8)
where 𝑝𝑔𝑜𝑎𝑙 is the desired steam pressure at the high-pressure evaporator outlet,
𝑇𝑔𝑜𝑎𝑙 is the desired steam temperature at high pressure the evaporator outlet, 𝑊𝑔𝑜𝑎𝑙 is the
target power in steam turbines, and 𝛼, 𝛽, and 𝛾 are the weights. The desired steam temperature at the high-pressure evaporator outlet and the target power in steam turbines
were set to 112 bar, 310 °C and 108 MW, respectively, while the weights and 𝛼, 𝛽, and
𝛾 were set to 0.001, 0.001, and 0.0001, respectively. Model constraints must be fulfilled
any time during the optimization horizon 𝑡 ∈ [𝑡0, 𝑡𝑓]. The steam pressure and temperature
at the high-pressure evaporator outlet, as well as the power of the steam turbines are
controlled by regulating the flue gases flow at the Heat Recovery Steam Generator
(HRSG) inlet and the steam flow at the superheater inlet. Likewise, it must be considered
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that the electrolytic solution of the electrowinning operates within a specific temperature
range and a flow rate of 1,000 (m3/h) [149].
64 ≤ 𝑇𝑒𝑠 ≤ 66 °𝐶 (6.9)
In addition, the positions of regulating valves of the gas turbine exhaust gases in the
splitter system, the hot flue gases regulating valve in the electrowinning process inlet and
the regulating valve of the hot flue gases at the Heat Recovery Steam Generator (HRSG)
inlet are assumed to take discrete values of opening per minute between 0 and 1.
0 ≤ 𝑉𝑏𝑦𝑝𝑎𝑠𝑠 ≤ 1 (6.10)
0 ≤ 𝑉𝑐𝑜𝑔𝑒𝑛 ≤ 1 (6.11)
0 ≤ 𝑉𝐻𝑅𝑆𝐺 ≤ 1 (6.12)
Meanwhile, the throttle valve that regulates the steam flow that enters the high-
pressure superheaters is assumed to take discrete values between 0 and 1.
0 ≤ 𝑉𝑆𝐻𝑇 ≤ 1 (6.13)
The regulating valves of the gas turbine exhaust gases in the splitter system, the hot
flue gases regulating valve in the electrowinning process inlet, and the regulating valve
of the hot flue gases at the Heat Recovery Steam Generator (HRSG) inlet are shown in
Figure 6.12.
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Figure 6.12. Gas turbine exhaust gases flow regulation system in the CHP system.
174
In order to avoid sudden changes in the state variables, the gas turbine exhaust gases
flow rate at the Heat Recovery Steam Generator (HRSG) inlet is constrained using the
ramping rate parameter [28]:
0 𝑀𝑊
𝑚𝑖𝑛≤𝑑𝑄
𝑑𝑡≤ 20
𝑀𝑊
𝑚𝑖𝑛 (6.14)
Moreover, large thermomechanical stresses must be avoided in the high-pressure
superheater header thick wall. From the steam pressure (𝑝𝑉𝐻𝑃𝑆𝐻), metal temperature
(𝑇𝑀𝐻𝑃𝑆𝐻) and steam temperature (𝑇𝑉𝐻𝑃𝑆𝐻) profiles in the superheater header, mechanical
and thermal stresses can be determined for the critical zone prone to failure in the header.
Using the superposition method, the thermal and mechanical effects are coupled for each
node of the superheater surrogate model. Then, the thermomechanical stresses in the
header can be estimated in a computationally efficient way and the structural integrity
constraint of the dynamic optimization problem is evaluated, which are constrained as
follows:
−200𝑁
𝑚𝑚2≤ 𝜎𝑆𝐻𝑇𝑀𝑆 ≤ 200
𝑁
𝑚𝑚2 (6.15)
As explained in Case study 1, the solution using the SATAS algorithm is represented
by three chromosomes. The first chromosome represents the sequence of actions. The
second chromosome represents the execution time per action, and the third chromosome
represents the number of times that the pair (action, execution time) is repeated. Each
element in the first chromosome is an integer that points to a combination of the valve
position of the throttle valve that regulates the steam flow that enters the high-pressure
superheaters and the ramping rate at the Heat Recovery Steam Generator (HRSG) inlet.
Table 6.3 shows the set of actions considered for this problem as a combining discrete
value of the heat flow rate in the HSRG inlet and the superheater throttle valve steam flow
rate.
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Table 6.3. Combinations of the heat flow rate in the HSRG inlet and steam flow rate in the superheater for each action.
Action Ramping Rate [MW/min]
Valve Position
1 10 0.8 2 10 0.9 3 10 1.0 4 15 0.8 5 15 0.9 6 15 1.0 7 20 0.8 8 20 0.9 9 20 1.0
The experiments considered three action durations (60, 120, and 180 s) and three
positions for the throttle valve (valve 80% open, valve 90% open, and valve completely
open). As a result, nine different actions were obtained, resulting from the combination of
three valve positions for the two valves (the case of both valves closed was not
considered). The repetition parameter was set to take integer values from 0 to 10. The
length of the sequence is fixed to 9 elements.
The optimization algorithm was initiated with a randomly generated solution and the
termination criteria were set to 480 iterations. The optimization process of the SATAS
algorithm generates new solutions through the neighborhood operator (NOP). The NOP
takes an existing solution and randomly changes one of the sequences (operator, time,
and repetition). All the experiments were carried out on a 3.4 GHz Intel Xeon E3-1245 V2
computer with 16 GB of RAM, running Windows 10 pro.
The operation of the gas turbine follows the operation profile reported by Hefni and
Bouskela [52]. The operation of the steam turbines is carried out by adding an adiabatic
splitter that diverts part of the gas turbine exhaust gases to a heat exchanger used by the
mining process, and the remaining gas turbine exhaust gases are delivered to the steam
turbine. We call this operational scheme as a baseline case study.
Figure 6.13 shows the operation of the cogeneration system in terms of the flow
required by the cogeneration system and the flow available for electrical power generation
in steam turbines, during the cyclic operation.
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Figure 6.13. Gas turbine exhaust gases flow required by the cogeneration system (blue) and flow available for the operation of steam turbines (red) in the case of a cyclic operation study.
The gas turbine exhaust gases flow diverted to the electrowinning process heat an
electrolytic solution and keep it at 65 °C. As described in Chapter 4, such an electrolytic
solution is used in the electrowinning process to produce high purity copper cathodes in
a copper mine [149]. Figure 6.14 shows the temperature (red) and enthalpy (blue) of the
electrolytic solution during the cyclic operation case study of the combined cycle power
plant coupled to a cogeneration plant. In the same way, Figure 6.15 shows the control
profiles of the regulating valve for the gas turbine exhaust gases in the electrowinning
process inlet during the cyclic operation case study of the combined cycle power plant
coupled to a cogeneration plant.
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Figure 6.14. Profiles of temperature and enthalpy of the electrolytic solution during the cyclic operation case study of the San Isidro II combined cycle power plant coupled to a cogeneration plant.
Figure 6.15. Control profiles of the regulating valve for the gas turbine exhaust gases in the electrowinning process inlet during the cyclic operation case study of the San Isidro II combined cycle power plant coupled to a cogeneration plant.
Figure 6.16 shows the distance from the current state to the goal state throughout the
simulation, that is, how the characteristic state variables of the objective function getting
closer to their desired state for the baseline case study and the optimized profile using
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the SATAS optimization algorithm for the cyclic operation case study of the combined
cycle power plant coupled to a cogeneration plant.
Figure 6.16. Comparison of the distance from the current state to the goal state overtime for the baseline case study (blue) and optimized profile using the SATAS optimization algorithm for the cyclic operation case study.
Figures 6.17 to 6.24 show the comparison of the results of this research with the
baseline case study developed based on the combined cycle power plant simulation
model developed by Hefni and Bouskela [52], the operational data of San Isidro II power
plant and the thermal energy requirements by the electrowinning process and optimized
profile using the proposed dynamic optimization framework. In these figures, blue lines
correspond to the baseline model, while the red lines correspond to the optimized profile
according to the dynamic optimization framework proposed in this research using the
SATAS algorithm.
Figure 6.17 shows the maximum power generated in the steam turbines during the
cyclic operation process. Figures 6.18 and 6.19 show the comparison of the operating
profiles of steam pressure and temperature at the high-pressure evaporator outlet,
respectively.
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Figure 6.17. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red
line) for the power generated in the steam turbines.
Figure 6.18. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the steam pressure at the high-pressure evaporator outlet.
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Figure 6.19. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the steam temperature at the high-pressure evaporator outlet.
For the power generated in the steam turbines (Figure 6.17) and the characteristic
state variables of the system for this case study (Figures 6.18 and 6.19), it can be
observed that the proposed optimization framework using the SATAS optimization
algorithm can achieve the desired operation goal in less time than the baseline model.
Likewise, the proposed framework was capable of generating the sequence of operations
of the throttle valve that regulates the steam flow that enters in the high-pressure
superheaters and the regulating valve of the gas turbine exhaust gases at the inlet of
Heat Recovery Steam Generator (HRSG) that regulates the ramping rate load in the
steam turbines.
In the same way, Figure 6.20 shows the operating profiles of the throttle valve that
regulates the steam flow that enters the high-pressure superheaters and Figure 6.21
shows the ramping rate of flow flue gases in the Heat Recovery Steam Generator
(HRSG).
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Figure 6.20. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the throttle valve that regulates the steam flow that enters the HP superheaters.
Figure 6.21. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the ramping rate of flow flue gases in the Heat Recovery Steam Generator (HRSG).
For the baseline model (Figure 6.20) the throttle valve that regulates the steam flow
that enters the high-pressure superheaters remained stable and in the same position
182
during the entire cyclic operation process for the baseline model. In contrast, the
proposed dynamic optimization framework using the SATAS optimization algorithm
suggests that the steam flow control valve should be operated sequentially and gradually
to achieve the goal state efficiently, generating stable and continuous profiles for the state
variables.
Similarly, the supply of hot flue gases to the Heat Recovery Steam Generator (HRSG)
is carrying out using a constant ramping rate for the baseline model until to reach the goal
state as shown in Figures 6.21. In the case of the proposed framework, the hot flue gases
are continuously applied and gradually increased using different ramping rates until the
goal state reached.
Figures 6.22 and 6.23 show the comparison of thermomechanical stresses in the two
main critical zones prone to failure in the superheater header.
Figure 6.22. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the thermomechanical stresses in critical zone 1 that are prone to failure.
183
Figure 6.23. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the thermomechanical stresses in critical zone 2 that are prone to failure.
In order to avoid hazardous scenarios in which the proposed procedures could result
infeasible from a decrease of useful life in the critical component, the high-pressure
superheater header structural integrity constraint must be monitored. The
thermomechanical stresses profiles generated by the proposed dynamic optimization
algorithm for both main critical zones of the header have a comparable pattern, shape,
and magnitude as in the baseline model, thus useful life of the thick-walled components
must be similar.
Table 6.4 shows a comparison of the thermomechanical useful life consumption and
fatigue damage in the superheater header for the baseline case study and the optimized
procedure using the SATAS optimization algorithm for the cyclic operation case study of
the combined cycle power plant coupled to a cogeneration plant. The useful life estimation
in the header was carried out based on methodology used in case study 1.
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Table 6.4. Comparison of the useful life consumption and fatigue damage in the superheater header for the cyclic operation case study of the combined cycle power plant coupled to a cogeneration plant.
Model Damage [%] Increase in life consumption [%] Residual life [%]
Baseline Model 41.33 0.00 50.86
SATAS 49.14 7.82 58.67 In this context, the profile generated by the SATAS optimization algorithm minimize
the time of cyclic operation of the combined cycle power plant by 21% with a decrease in
the useful life of 7.82% percent compared to the baseline model.
Finally, Figure 6.24 the maximum power generated in the steam turbines during the
cyclic operation process.
Figure 6.24. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the power generated in the gas and steam turbines.
Regarding the gas turbine power, it can be observed that the profiles for the baseline
model and the optimized has the same behavior, this is because the gas turbine
operational optimization was not part of this research.
In summary, the proposed dynamic optimization framework is capable of designing
the operation sequence of a CHP system under cyclic operation scheme, which supplies
185
thermal energy to an electrowinning process for to produce high purity copper cathodes
in a copper mine and minimized the load change times for the steam cycle of a combined
cycle power plant to satisfy the electrical power required by the network in the shortest
time possible. Thus, the proposed framework identifies the corresponding control actions
and their sequence to design integrally the optimal operating procedure, without
compromising the structural integrity of critical components using a computationally
efficient model. Likewise, a scalable tool was developed focused on being implemented
other thermal power plant processes and applications, whose applications involved
advanced dynamic simulation and optimization techniques aimed at improving the
designs of the operating procedures.
186
7. Chapter Seven
Conclusions and Future Work
To deal with the challenge of a balance between the large-scale introduction of variable
renewable energies and intermittent energy demand scenarios for current electrical
systems known as power system operational flexibility. We address this problem of
electric power system operational flexibility from the power generation area using a power
plant level approach. From this approach, the problem is addressed as an operational
design strategy using advanced model, simulation and optimization techniques that focus
on minimizing the time needed to take the power plant from an initial state to the goal
state along with their corresponding sequence of control valves operations without
compromising the structural integrity of critical plant components..
In this context, a methodology to the synthesis of optimum operating procedures of
thermal power plants which finds the optimal control valves sequences that minimize its
operating times was developed. For this methodology, a dynamic optimization framework
was developed. This framework is based on the implementation of a metaheuristic
optimization algorithm coupled with a dynamic simulation model, using the modeling and
simulation environment OpenModelica and a surrogate model to estimate in a
computationally efficient way the structural integrity constraint of the dynamic optimization
problem. An open interface based on the C# code is developed to connect the dynamic
simulator with the optimization module and the surrogate model. Also, dynamic simulation
models of a drum boiler, combined cycle power plant, and combined heat and power
system were developed using the OpenModelica environment and validated against
information published in the literature. Likewise, two metaheuristic optimization
algorithms were implemented in the optimization framework. These optimization
algorithms are a micro genetic algorithm (mGA) based on Batres [112] that is
characterized by small populations of individuals, and a hybrid algorithm SATAS that
combines the feature of the cooling element from the simulated annealing algorithm and
the efficient computational performance provided from the tabu search algorithm. Also, a
surrogate model based on the finite element method simulations, response surfaces
187
models, and an artificial neural network model to estimate the efficient way the structural
integrity of the heat recovery steam generator superheater header was developed.
The developed dynamic optimization framework was implemented in two case
studies. The first case study focuses on managing the thermal power plant's flexible
operation based on the synthesis of the startup operating procedure of a drum boiler. The
second case study addresses the synthesis of an optimum operating strategy of a
combined heat and power system to improve the electric power system’s operational
flexibility.
For the first case study, the dynamic optimization problem was focused on the drum-
boiler startup aims at achieving a given state in terms of the drum-boiler internal pressure
and the output steam mass flow rate, in the shortest time possible, while avoiding
excessive thermal stresses. The two metaheuristic optimization algorithms were
implemented in the dynamic optimization framework, and according to their numerical
results, the optimal startup operation sequence that takes the drum boiler to the goal state
was reached in 35% less time compared to the baseline startup strategy for the micro
genetic algorithm (mGA) and 42% less time for SATAS algorithm.
Regarding the second case study, it was addressed through the CHP system cyclic
operation where the power plant steam turbines and the thermal energy generation for
the mining process are managed through a splitter system of the gas turbine exhaust
gases. At the beginning of the cyclic operation case study, steam turbines are generating
electrical power at baseload, while the cogeneration system is not under operation. Once
the steam turbine operation moves towards the minimum load, the cogeneration system
begins the generation process of thermal energy for the electrowinning process. When
the steam turbines reach their minimum load state, the cogeneration system must be
reaching the thermal energy production required by the electrowinning process. The next
stage of the cyclic operation case study consists of the steam turbines changing their load
toward a new baseload since some amount of gas turbine exhaust gas is used to generate
the thermal energy of the mining process. In this stage, we seek to increase the
operational flexibility of the CHP system by implementing the proposed dynamic
optimization framework coupled with the developed surrogate model, to produce
operating procedures that minimize the time needed to take the power plant from an initial
188
state (minimum load) to the goal state (baseload) along with their corresponding
sequence of control valves operations without compromising the structural integrity of
critical plant components. At the same time, the gas turbine exhaust gases must be
controlled to keep a stable and continuous generation of thermal energy for the mining
process.
The SATAS optimization algorithm was used in this case study under the optimization
framework since it provided the best results in the synthesis of the startup operating
procedure of a drum boiler case study. The developed surrogate model of the superheater
header was used to estimate in a computationally efficient way the structural integrity
constraint of the dynamic optimization problem through an open interface based on C#
code to connect with the optimization module.
From numerical results, it can be observed that the proposed dynamic optimization
framework was capable of designing the operation sequence of a CHP system under
cyclic operation scheme, which supplies thermal energy to an electrowinning process for
to produce high purity copper cathodes in a copper mine and minimized the load change
times for the steam cycle of a combined cycle power plant to satisfy the electrical power
required by the network in about 21% less time compared to the reference case study.
The proposed framework identifying the corresponding control actions and their sequence
to design integrally the optimal operating procedure, without compromising the structural
integrity of critical components using a computationally efficient model.
As future work, it is considered feasible to take advantage of the flexibility of the
methodology developed for other case studies that include the gas turbine power block
of the combined cycle plant, as well as other kinds of thermal power plants. Likewise,
different optimization algorithms can be tested and validated using the developed
optimization framework. Also, the integration of thermal energy storage systems within
the power cycle of the power plant can be carried out coupled with an optimal operational
management strategy of the CHP system to enhance its operational flexibility. The
operational management of the remaining heat of thermal power plants to supply thermal
energy in other industrial processes could be evaluated. Regarding the surrogate model,
it can extend it to other critical components of the power plant such as drums, steam
turbines, steam turbine casings, or high-pressure pipelines. Finally, this optimization
189
framework for the synthesis of operating procedures could be extended to other industrial
processes.
190
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Published papers
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Curriculum Vitae
Erik Rosado Tamariz is a researcher at the mechanical systems department in the National Electric and Clean Energies Institute (INEEL). He has attained his BSE in Mechanical Engineering and his MSc on Mechanical Engineering from Instituto Tecnologico de Veracruz. He has over 10 years of in-depth experience in energy industry and worked on several projects involving modeling, simulation and optimization of critical equipment of power plants, design and evaluation of operational performance of turbomachinery, analysis of equipment performance and its relationship with wear in steam and gas turbines. Also, is a part time professor at the Tecnologico de Monterrey in campus Cuernavaca in mechanical design and electrical power generation systems areas. He is currently undertaking a PhD project at the Tecnologico de Monterrey focuses at the development of optimal operating strategies of thermal power plants to improve their competitiveness in the liberalized energy markets.
https://www.researchgate.net/profile/Erik_Rosado